**The Database of Z4 Codes**

Check out the Database for Z4 Codes

My primary area of research is Algebraic
Coding Theory. I received my PhD from The Ohio State University.

Here is the abstract of my PhD thesis from OSU
web site.

My PhD advisor was Prof. Dijen Ray-Chaudhuri , the letter "C" in
BCH codes refers to him.

My areas of interest include:

- Algebraic and combinatorial constructions of codes with good parameters over finite fields and rings
- Cyclic codes and their generalizations
- Codes over Z_4 and more general rings
- Code-based cryptography
- Cryptography
- History of Mathematics and Science, especially in the Islamic World. Listen to my story here.
- Relationship between religion and science
- Mathematics Education/Pedagogy
- Theoretical Computer Science

Publications

Books

Miftah al-Hisab, Volume III: Algebra, Translation and Commentary, Springer/Birkhäuser, 2022 (joint work with L. Hammoudi and G. Bakbouk), ISBN 978-3-030-96614-0

Miftah al-Hisab, Volume II: Geometry, Translation and Commentary, Springer/Birkhäuser, 2020 (joint work with L. Hammoudi and G. Bakbouk), ISBN 978-3-030-61329-7

Miftah al-Hisab, Volume I: Arithmetic, Translation and Commentary, Springer/Birkhäuser, 2019 (joint work with L. Hammoudi), ISBN 978-3-030-14949-9

Algebraic Coding Theory and Cryptography

· H.
Ou-azzou, M. Najmeddine, N. Aydin, Liu, B. Ialou, E. M. Mouloua, Linear codes invariant under a linear endomorphism, accepted for publication in *Advances in Mathematics of Communication*, 2024.

· H. Ou-azzou, M. Najmeddine, N. Aydin, On the algebraic structure of quasi-polycyclic codes and new quantum codes, Quantum Information Processing, 23(3),2024.

· T.
Abualrub, S. Karbaski, N. Aydin and P. Liu*. Additive
polycyclic codes over F4 induced by nonbinary polynomials, Journal
of Applied Mathematics and Computing, 2023.

· S. R. Pandey*, N. Aydin, E. Z. Chen, F. Jönsson, K. Klonowska, New Results and Bounds on Codes over GF(19), accepted for publication in J. Information and Optimization Sciences, 2024.

·
H. Ou-azzou, M. Najmeddine, N. Aydin, E. M.
Mouloua, On the algebraic structure of (M,sigma,delta)-skew codes,
accepted for publication in *Journal of Algebra*, 2023.

·
H. Ou-azzou, M. Najmeddine, N. Aydin. Linear codes invariant under cyclic endomorphisms,
accepted for publication *in Journal of Algebra and Its Applications*,
2023.

·
A. Bellil, K. Guenda, N. Aydin, P. Liu*, T.
Aaron Gulliver. Constacyclic and quasi-twisted codes over
Zq[u]/< u^2-1> and new Z4-linear codes. *Advances in
Mathematics of Communications*, 2023 doi: 10.3934/amc.2023026

·
N. Aydin, T.Guidotti*, P. Liu*, Good
classical and quantum codes from multi-twisted codes, *Contemporary
Mathematics*, Algebra and Coding Theory, 785:7 2023,
https://doi.org/10.1090/conm/785/15771

·
N. Aydin, Y. Lu*, V. Onta*, An updated database of Z4 codes and an Open Problem about
Quasi-Cyclic Codes, In El-Hajji, S., Mesnager, S.,
Souidi, E.M. (eds) *Codes, Cryptology and Information Security*.
C2SI 2023. Lecture Notes in Computer Science, vol 13874. Springer, Cham.
https://doi.org/10.1007/978-3-031-33017-9_24

· B. Caliskan, N. Aydin, P. Liu*, Skew cyclic codes over Z4+uZ4+vZ4, Cryptogr. Commun., Vol 15, 845-858, (2023), https://doi.org/10.1007/s12095-023-00645-3

· F. Caliskan, R. Aksoy, N. Aydin, P. Liu*, Entanglement-Assisted Binary Quantum Codes from Skew Cyclic Codes over F_2 x (F_2+vF_2), accepted for publication in Quantum Information Processing.

· E. Z. Chen, N. Aydin, F. Jönsson, K. Klonowska, New Results and Bounds on codes over GF(17), JACODESMATH, 11(1), 2024, 27-39

·
Z. Hebbache, A. Kaya, N. Aydin, K. Guenda, On
Some Skew Codes over Zq+uZq, Discrete Mathematics, Algorithms, and
Applications, *16*(01), 2250186 (2024),https://doi.org/10.1142/S1793830922501865

·
D. Akre*, N. Aydin, M. Harrington*, S. Pandey*, A Generalization of
Cyclic Code
Equivalence Algorithm to Constacyclic Codes, *Des. Codes Cryptogr.* **91**, 763–777 (2023).
https://doi.org/10.1007/s10623-022-01124-1

·
D. Akre*, N. Aydin, M. Harrington*, S. Pandey*, New Binary and Ternary Quasi-Cyclic Codes with Good
Properties, *Comp. Appl. Math.* **42**,
102 (2023). https://doi.org/10.1007/s40314-022-01946-8

· S. Pandey*, N. Aydin, M. Harrington*, D. Akre*, A Generalization of the ASR Search Algorithm to 2-Generator Quasi-Twisted Codes, ISIT 2022.

· N. Aydin, P. Liu*, B. Yoshino*. Polycyclic Codes Associated with Trinomials: Good Codes and Open Question, Designs,Codes, and Cryptography 2022.

· A. S. Karbaski, T. Abualrub, N. Aydin and P. Liu*. Additive Polycyclic Codes over F_4 Induced by Binary Vectors and Some Optimal Codes, Advances in Mathematics of Communications, 2022.

· N. Aydin, P. Liu*, B. Yoshino*. A Database of Quantum Codes, J. of Algebra Combinatorics Discrete Structures and Applications, 2021.

· N. Aydin and O. R. Vandenberg* A New Algorithm for Equivalence of Cyclic Codes and Its Applications, accepted for publication in Applicable Algebra In Engineering, Communication and Computing, 2021,[available online] DOI 10.1007/s00200-021-00525-4

·
A. Dertli, Y. Cengellenmis, and N. Aydin, On Skew Cyclic Codes over a mixed alphabet and their
applications to DNA codes, *Discrete Mathematics,
Algorithms and Applications, 2021, **https://doi.org/10.1142/S1793830921501433*

* *

· *N.
Aydin, B. Yildiz, and S. Uludag, **A Class of Weak Keys for the QC-MDPC Cryptosystem**,
2020 Algebraic and Combinatorial Coding Theory (ACCT), Albena,
Bulgaria, 2020, pp. 1-4, doi: 10.1109/ACCT51235.2020.9383383.*

* *

· *N.
Aydin, T. Guidotti*, and P. Liu*, **New Linear Codes as Quasi-Twisted Codes from Long
Constacyclic Code**, 2020 Algebraic and
Combinatorial Coding Theory (ACCT), Albena, Bulgaria, 2020, pp. 1-6,
doi: 10.1109/ACCT51235.2020.9383237.*

* *

· *N.
Benbelkacem, M. F. Ezerman, T. Abualrub, N. Aydin and A. Batoul, Skew
Cyclic Codes Over F_4 R, **Journal of Algebra and Its Applications**.
2250065, (2022), DOI: **10.1142/S0219498822500657*

* *

· *Y.
Cengellenmis, N. Aydin, A. Dertli, **Reversible DNA Codes from Skew Cyclic Codes over a
Ring of Order 256**, Journal of Algebra
Combinatorics Discrete Structures and Applications, Vol 8(1), 1-8,
2021.*

* *

· *T.
Abualrub, N. Aydin, I. Aydogdu, Optimal Binary Codes Derived from
F2F4-additive Cyclic Codes, **Journal of Applied Mathematics and Computing, **64,71–87
(2020). https://doi.org/10.1007/s12190-020-01344-5*

* *

· *N.
Aydin,T Guidotti*, P.Liu*, A Shaikh*, O VandenBerg*, **Some Generalizations of the ASR Search Algorithm for
Quasi-Twisted Codes**, Involve, Vol 13(1), 2020,
137-148.*

* *

· *
A. Melakhessou, N. Aydin, Z. Hebbache,K. Guenda, **Zq(Zq+uZq)-linear skew constacyclic codes**,
Journal of Algebra Combinatorics Discrete Structures and Applications,
17(1), 2020, 85-101.*

* *

· *N.
Aydin,Y. Cengellenmis, A. Dertli,S. T. Dougherty, E. Salturk **Skew
cyclic and skew constacyclic codes over the local Frobenius
non-chain rings of order 16**, Advances in
Mathematics of Communication, 14(1), Feb 2020, 53-67.*

* *

· *N.
Aydin, “**Some new linear codes from skew cyclic codes and
computer algebra challenges**”, Applicable Algebra
in Engineering Communication and Computing, March 2019, **https://doi.org/10.1007/s00200-019-00383-1*

* *

· *
N. Aydin, J. Lambrinos*,Oliver VandenBerg*, “**On Equivalence of Cyclic Codes, Generalization of a
Quasi-Twisted Search Algorithm, and New Linear Codes**”,
Designs, Codes and Cryptography, 2019, DOI:10.1007/s10623-019-00613-0*

* *

· *
N. Aydin,G. Bakbouk*, J. Lambrinos*, “**New Linear Codes over non-Prime Fields**”,
**Cryptography and Communications**,
11(5), 891-902, 2019, DOI: 10.1007/s12095-018-0333-2*

* *

· * N, Aydin, D. Foret*, “New Linear Codes over GF(3),
GF(11), and GF(13) ”, **Journal of Algebra Combinatorics Discrete Structures
and Applications**, 6 (1), 13-20, 2019.*

* *

· *M. Ozen, F. Z. Uzekmek, N, Aydin, N. T. Ozzaim, “**One generator quasi-cyclic codes over F2+v**
”, J. Appl Math & Informatics, Vol 36, 2018, 359-378,
https://doi.org/10.14317/jami.2018.359 *

* *

· *Y.
Cengellenmis, A. Dertli, N. Aydin, “**Some constacyclic codes over Z4[ u]/ < u^2>, new
Gray maps, and new quaternary cod**”, Algebra
Colloquim, 25(3), 2018, 369-376*

* *

· *R.
Dastbasteh, H. Mousavi, T. Abualrub, N. Aydin, J. Haghighat, “**Skew cyclic codes over F_p+uF**”, Int.
J. of Information and Coding Theory, Vol 5. No. 1, 2018, 81--99.*

* *

· *N.
Aydin, A. Dertli, Y. Cengellenmis, “On some constacyclic codes
over Z4[ u]/ < u^2-1>, their Z4 images, and new codes”,
Des. Codes Cryptogr. 86(6), 2018, :1249–1255, **DOI: 10.1007/s10623-017-0392-y*

* *

· *M.
Ozen, T. Ozzaim, N. Aydin, “**Cyclic codes over Z4 + uZ4 + u^2**”, Turkish
J. Math. 41(5), 2017, 1235-1247, **DOI: 10.3906/mat-1602-35*

* *

· *A.
Batoul, K. Guenda, T. A. Gulliver, N. Aydin, “**Constacyclic codes over finite principal ideal rin**”
International Conference on Codes, Cryptology, and Information
Security C2SI 2017, Springer LNCS 10194, pp 161-175,** DOI 10.1007/978-3-319-55589-8_11*

* *

· *A.
Batoul, K. Guenda, T. A. Gulliver, N. Aydin, “On isodual cyclic
codes over finite chain rings” International Conference on
Codes, Cryptology, and Information Security C2SI 2017, Springer LNCS
10194, pp 176-194, **DOI 10.1007/978-3-319-55589-8_12.*

* *

· *N.
Aydin, N. Connolly*, J. Murphree* “New binary linear codes from QC
codes and an augmentation algorithm”AAEC. 28(4) 339-350, August 2017,
DOI **https://doi.org/10.1007/s00200-017-0327-x*

* *

· *N.
Aydin, A. Halilovic, “ A Generalization of Quasi-twisted Codes:
Multi-twisted codes”, Finite Fields and Their Applications, 45 (2017),
96-106, DOI: **http://dx.doi.org/10.1016/j.ffa.2016.12.002*

* *

· *M. Shi, L. Qian, L. Sok, N. Aydin, P. Sole“ On
constacyclic codes over Z4[u]/<u^2-1>”, Finite Fields and Their
Applications, 45 (2017), 86–95, DOI: **http://dx.doi.org/10.1016/j.ffa.2016.11.016*

* *

· *N. Aydin, N. Connolly*, and M. Grassl,“Some results on the
structure of constacyclic codes and new linear codes over GF(7) from
quasi-twisted codes”, Advances in Mathematics of Communication, Vol
11(1), 2017, 245-258, **DOI: 10.3934/amc.2017016*

*.*

· *T. Abualrub, N. Aydin,“Additive Cyclic Codes over Mixed
Alphabets and the Football Pool Problem”, Discrete Math. Algorithm.
Appl. **09**, 1750010 (2017) [13
pages] DOI: **http://dx.doi.org/10.1142/S1793830917500100*

* *

· *N. Aydin, and T.Abualrub. “Optimal quantum codes from
additive skew cyclic codes”, Discrete Mathematics, Algorithms, and
Applications, 8(1), 2016 DOI:10.**10.1142/S1793830916500373**.*

* *

· *M. Ozen, F. Z. Uzekmek, N, Aydin, N. T. Ozzaim, “Cyclic
and some constacylic codes over the ring Z4[u]/<u^2-1> ”, Finite
Fields and Their Applications, Vol 38, 2016, 27-39, **https://doi.org/10.1016/j.ffa.2015.12.003*

* *

· *R. K. Bandi, M. Bhaintwal, and N. Aydin. “A mass formula
for negacyclic codes of length 2^k and some good negacyclic codes over
Z4+uZ4”, Cryptography and Communications, 2016,** DOI: 10.1007/s12095-015-0172-3**.*

* *

· * E. Chen and N. Aydin, "A database of linear codes over
F13 with minimum distance bounds and new quasi-twisted codes from a
heuristic search algorithm", **JACODESMATH** (Journal of Algebra,
Combinatorics, Discrete Structures and Applications), Vol 2 (1),
2015,1-16.*

* *

· * E. Chen and N. Aydin, "New quasi-twisted codes over
F11-minimum distance bounds and a new database", **J. of Information and Optimization Sciences**,
Vol 36 (1-2), 2015,129-157.*

* *

· * B. Yildiz and N. Aydin, “ On Cyclic codes over Z_4+uZ4
and their Z4-images”, **International Journal of Information and Coding Theory**,
Vol 2 (4), 2014, 226-237.*

* *

· * N. Aydin, J. Murphree* “New Linear Codes from
Constacyclic Codes” **Journal of the Franklin Institute**,
Vol 351 (3), March 2014, 1691-1699.*

* *

· * S. Karadeniz, B. Yildiz and N. Aydin, “ Extremal
binary self-dual codes of lengths 64 and 66 from four
circulant constructions over F2+uF2", **FILOMAT**, Vol 28 (5), 2014, 937-945.*

* *

· * T. Abualrub, I. Siap and N. Aydin, “Z_2Z_4-additive
cyclic codes”, **IEEE Transactions on Information Theor**y,
Vol 60 (3), March 2014, 1508-1514.*

* *

·
*N. Aydin, S. Karadeniz, and B. Yildiz, “Some
new binary quasi-cyclic codes from codes over the ring F2 +
uF2+vF2+uvF2”, **Applicable Algebra in Engineering, Communication and
Computing.** Vol 24 (5), Nov 2013, 355-367.*

* *

·
*T. Abualrub, N. Aydin, and P. Seneviratne,
“Theta-Cyclic Codes Over F2 + vF2”, **Australasian Journal of Combinatorics**,
Vol 54, October 2012, 115-126,*

* *

·
*I. Siap, T. Abualrub, N. Aydin, and P.
Seneviratne, “Skew quasi-cyclic codes of arbitrary length” **International Journal of Information and Coding Theory**,
Vol 2 (1), 2011, 10-20.*

* *

·
*I. Siap, T. Abualrub and N. Aydin “Quaternary
quasi-cyclic codes with even length components” **Ars Combinatoria** Vol CI, July 2011
pp. 425-434*

* *

·
*N. Aydin, and T. A. Gulliver, “Some good
cyclic and quasi-twisted Z4-linear codes”,** Ars Combinatoria**, Vol XCIX, Apr
2011, pp. 503-518.*

* *

· * R. Ackerman*, and N. Aydin, “**New quinary linear codes from quasi-twisted codes and
their dual**” Applied Mathematics Letters, Vol 24,
No 4, pp 512-515, April 2011.*

* *

· * T. Abualrub, A. Ghrayeb, N. Aydin , and I. Siap, “On the
construction of skew quasi-cyclic codes” **IEEE Transactions on Information Theory**,
Vol. 56, No. 5, pp. 2081-2090, May 2010.*

* *

·
*N. Aydin, T. Asamov*, “Search for good linear
codes in the class of quasi-cyclic and related codes” **Selected Topics in Information and Coding Theory**,
Edited Book, I. Woungang, S. Misra, S. Chandra Misra (Eds.), Series on
Coding and Cryptology, World Scientific Publishing,
ISBN:978-981-283-716-5/981-283-716-7, March 2010, 724 pages.*

* *

·
*N. Aydin , and T. Asamov*, “A Database of Z4
Codes”, **J. of Combinatorics, Information & System Sciences**
(JCISS), Vol. 34 No. 1-4 Comb, 2009, p: 1-12.*

* *

·
*T. Asamov*, and N. Aydin. “A search
algorithm for linear codes: progressive dimension growth”,** Designs, Codes and Cryptography**, **Vol. 45, No 2, pp.
213-217, November 2007.*

* *

·
*N Aydin, T. Asamov*, and T. A. Gulliver
“Some open problems on quasi-twisted and related code
constructions and good quaternary codes”, In Proceedings of
International Symposium on Information Theory (ISIT 2007), June 24-29
2007, Nice, France, 856-860.*

* *

·
*T. Asamov*, and N. Aydin, “LDPC
codes of arbitrary girth”, In Proceedings of the 10*^{th}* Canadian Workshop on Information Theory (CWIT 2007), June
6-8 2007, Edmonton, Alberta, Canada, 69-72.*

* *

·
*N. Aydin and D. Ray-Chaudhuri “On some
classes of optimal and near-optimal polynomial codes”, **Finite Fields and Their Applications*.*
Vol. 10, No. 1,** **pp.** **24-35, January 2004.*

* *

·
*N. Aydin and I. Siap “New
quasi-cyclic codes over F5” **Applied Mathematics Letters**, Vol 15,
No 7, pp 833-836, October 2002*

* *

·
*N. Aydin and D. Ray-Chaudhuri “Quasi-cyclic
codes over Z4 and some new binary codes” **IEEE Transactions on Information Theory**
**Vol. 48, No. 7, pp. 2065-2069, July 2002.*

* *

·
*N. Aydin, I. Siap and D. Ray-Chaudhuri “The
structure of 1-generator quasi-twisted codes and new linear codes”,**Designs Codes and Cryptography**, **Vol.
24, No. 3, pp. 313-326, December 2001**.*

* *

·
*I. Siap, N. Aydin and D. Ray-Chaudhuri “New
1-generator quasi-twisted codes over GF(5)” In Codes** **and
Association Schemes*** **(Piscataway, NJ, 1999)

* *

·
*I. Siap, N. Aydin and D. Ray-Chaudhuri “New
ternary quasi-cyclic codes with improved minimum distances”,**IEEE Transaction on Information Theory**,
Vol. 46, No. 4, pp. 1554-1558, July 2000.*

* *

** denotes a Kenyon undergraduate*

*History of Science*

*• N. Aydin, "**The Legacy of Islamic/Arabic
Mathematics**",
MAA Focus, April/May 2024.*

*• N. Aydin, "**The Role of Religion in the Development of
Mathematical Sciences in Medieval Islamic Civilization**",
Muslim Heritage, 2021.*

*• N. Aydin and L. Hammoudi, "**Root Extraction by Al-Kashi and Stevin**",
Archive for History of Exact Sciences,** Vol 69 (3)**, pp 291-310, May 2015.
DOI 10.1007/s00407-015-0150-3*

*• Algebra, in The Oxford Encyclopedia
of Philosophy, Science, and Technology in Islam, May 2014.*

*• Geometry, in The Oxford
Encyclopedia of Philosophy, Science, and Technology in Islam, May
2014.*

*• N. Aydin and M.Rihtim “A striking
example of connections between Renaissance Europe and the Muslim
World: Copernicus and Tusi” Proceedings of the international
conference devoted to the 810th years of Nasireddin Tousi, June 2011,
Baku-Azerbaijan, pp. 53-64, National Academy of Sciences of
Azerbaijan.*

*Computer Science*

*• N. Aydin and P. A. Sivilotti
“Remote Belief: Preserving Volition for Loosely-Coupled Processes”, in
proceedings of **ICDCS
2003, 23 rd International Conference on Distributed Computing
Systems, Providence, Rhode Island, pp. 434-440, May 19-22, 2003*

*Pedagogy/Mathematics Education*

*• N. Aydin, “**Impacts of a unique course on the history of
mathematics in the Islamic World**”, MAA
Convergence, July 2017*

*• A. S. Ozdemir, E. Guler, N. Aydin,
“**Effects of Cryptographic Activities on Understanding
Modular Arithmetic**”, Turkish Journal of Computer
and Mathematics Education, Vol.2 No.3, 247-256, 2011.*

*• N. Aydin **“Enhancing Undergraduate Curriculum via Coding Theory
and Cryptography"**, **PRIMUS** (Problems, Resources and
Issues in mathematic undergraduate studies) Volume 19 Issue 3,
296-309, May 2009.*

*• N. Aydin and E. Halat “The impacts
of undergraduate mathematics courses on college students' geometric
reasoning stages”, **Montana Mathematics Enthusiasts, **Vol
6, Nos 1&2, 151-164, 2009.*

*• E. Halat, E. Jakubowski E. and N.
Aydin “**Reform-Based Curriculum and Motivation in Geometry**”,
**Eurasia
Journal of Mathematics, Science and Technology Education**,
Vol 4, No 3, 285-292, 2008.*

*• N. Aydin “Elliptic Curve
Cryptography”, A Computational Science Module developed as part of an
NSF grant. December 2011.*

*• N. Aydin “Public Key Cryptography
and the RSA Cryptosystem”, A Computational Science Module developed as
part of an NSF grant. July 2009.*

*• N. Aydin “An Introduction to
Coding Theory via Hamming Codes”, A Computational Science Module
developed as part of an NSF grant. August 2007.*

*Conference Presentations*

· *"Coding Theory: Past, Present, and Future", Invited Talk, International Urdu Science Conference, MANUU, Hyderabad, India, March 2024.*

·
*"Coding Theory as Pure and Applied
Mathematics: Its Connections and Applications", Invited Keynote
Speech, ICDMC-2023, Bengaluru India, 20 December 2023.*

·
*"Pure Math, Applied Math, Information Theory
and the Place of Algebra in Mathematics", Invited Talk (virtual),First
IIIMT-Algebra Forum Conference, 16 December 2023.*

· * “ On Some Special Matrices and Their Application to Code
Construction”, ALCOCRYPT 2023, Marseille, France, February 2023
(presented by K. Guenda) ” **.*

· * “The Additive polycyclic codes over F4 II: The general
case”, ALCOCRYPT 2023, Marseille, France, February 2023 (presented by
T. Abualrub) ” **.*

· * “The Need for Teaching a More Accurate and Inclusive
History of Mathematics and Science ”, Leiden University, March 2023**.*

· * “The Need for Teaching a More Accurate and Inclusive
History of Mathematics and Science ”, MAA MathFest, August 2022
(presented in the session Pursuing Justice in and through Mathematics)*

· * “Algebraic Coding Theory and Code-Based Cryptography”,
MAA MathFest, August 2022 (presented in the session Coding Theory and
its Applications)*

· * “A Generalization of the ASR Search Algorithm to
2-Generator Quasi-Twisted Codes” ISIT 2022, June 2022 (N. Aydin*,**
D. Akre, M. Harrington*, and S. Pandey* **).*

· * “**A Generalization of the ASR Search Algorithm to
2-Generator Quasi-Twisted Codes**” Joint
Mathematics Meetings, 2020, April 2022 (N. Aydin*,** D. Akre,
M. Harrington, and S. Pandey**).*

· * “**The Need for Including Islamic Math and Science in
School Curricula**", Joint Mathematics Meetings,
2020, April 2022.*

· * “New Linear Codes as QT codes from Long Constacyclic
Codes”, ACCT 2020 (17th Int Workshop on Algebraic and Combinatorial
Coding Theory), Bulgaria, October 2020 (N. Aydin*,** T.
Guidotti and P. Liu**).*

·
*“ Al-Kashi's Miftah al-Hisab: a 21st century
translation and reading”, Joint Mathematics Meetings 2020, in **AMS Special Session on Current Areas of Interest in
the Mathematical Sciences of Medieval Islam**,
Denver, CO, USA January 2020 (N. Aydin and L. Hammodi*).*

·
*“A New Algorithm for Equivalence of Cyclic
Codes and Its Applications”, **AMS Contributed Paper Session on Computer Science,
Programming, Information and Related Topics**,
Joint Mathematics Meetings 2020, in, Denver, CO, USA January 2020 (N
Aydin, and **R. O. VandenBerg***).*

·
*“New Results on Equivalence of Cyclic Codes
and a Generalization of a Search Algorithm", Southeastern
International Conference on Combinatorics, Graph Theory, and
Computing, Florida Atlantic University, FL, March 2019 (N. Aydin and **R.
O. VandenBerg***)*

·
*“Code-Based Crytography for the
Internet-of-Things", 4 hour tutorial in **IEEE Consumer Communications & Networking
Conference**, Las Vegas, NV, January 2019 (N.
Aydin, S. Uludag, and B. Yildiz).*

·
*“A Generalization of Quasi-Twisted Codes:
Muti-twisted Codes", **AMS Sectional Meeting** (#1136), The
Ohio StateUniversity, Columbus, OH, March 2018.*

·
*“ Translation of Miftah al-Hisab", Midwest
History of Math Conference and ORESME Joint Meeting, Wabash College,
Crawfordsville, IN, Sep 2017.*

·
*“ Recent Methods of Constructing New Linear
Codes over Z4”, Mathematical Congress of the Americas, in Special
Session on **Finite
Algebraic Combinatorics and Applications**,
Montreal, Canada, July 2017.*

·
*“ Legacy of Al-Kashi: Why does it matter in
the 21st century”, Joint Mathematics Meetings 2016, in **AMS Special Session on Current Areas of Interest in
the Mathematical Sciences of Medieval Islam**,
Seattle, WA, USA January 2016 (**N. Aydin***, and L.
Hammoudi)*

·
*“ New Binary Linear Codes from Quasi-Cyclic
Codes and an Augmentation Algorithm", The International Conference on
Coding Theory and Cryptography (ICCC 2015), USTHB, Algiers, Algeria,
November 2015.*

·
*“ The Legacy of Islamic Science in the Modern
World: A Few Examples”, Grand Dialogue in Religion & Science,
Grand Valley State University, Grand Rapids, MI, June 2015.*

·
*“Computer Algebra Challenges for Constructing
Skew Cyclic Codes”, ACA (Applications of Computer Algebra) 2014,
Fordham University, NY, July 2014.*

* *

·
*“New Databases of Linear Codes over GF(11)
and GF(13)”, Karatekin Mathematics Days, at Cankiri Karatekin
University, Turkey, June 2014.*

* *

·
*“A History of Mathematics Course for the
Liberal Arts”, MAA-Ohio Section Spring 2014 meeting, University
of Toledo, Toledo, OH, April 2014.*

* *

·
*“Islam, History and Mathematical Sciences”,
Online lecture, Hast-o-Neest Institute of Traditional Studies
& Arts, Pakistan, January 2013.*

* *

·
*“Recent Results in Skew Cyclic Codes”,
31st Ohio State-Denison Mathematics Conference, The Ohio State
University , Columbus, OH May 2012.*

* *

·
*“Skew Additive Cyclic Codes", ICAAA
2011, International Conference on Applied Analysis and Algebra, Yildiz
Technical University , Istanbul Turkey, July 2011.*

* *

· * “A Striking Example to Connections Between Europe and the
Muslim World: Copernicus and Tusi” International conference on
the history, philosophy of science and technology devoted to the
810-th anniversary of Nasireddin Tousi, June 2011, Baku, Azerbaijan*

* *

·
*“A Database of Z4 Codes”, The
first Int. Conference on Mathematics and Statistics, American
University of Sharjah, Sharjah, UAE. March 2010.*

* *

·
*“Search for Good Linear Codes over Z_4 and a
New Database”, International Conference on Algebra and its
Applications, Ohio University, Athens, OH, June 2008.*

* *

·
*“Search for Good Linear Codes”, 29th
OSU-Denison Conference, Special Session in Combinatorics, The Ohio
State University, Columbus, OH, May 2008.*

* *

·
*“Some open problems on quasi-twisted and
related code constructions and good quaternary codes”, International
Symposium on Information Theory, Nice, France, June 2007.*

* *

·
*“Enhancing undergraduate mathematics
curriculum via coding theory and cryptography”, Poster presentation,
in 3*^{rd}*
International Conference on the Teaching of Mathematics at the
Undergraduate Level, Istanbul, Turkey, July 2006.*

* *

·
*“Enhancing undergraduate mathematics
curriculum via coding theory and cryptography”, MAA Spring 06
meeting, in Ohio Project Next Section, University of Akron,
Akron, OH, March 2006.*

* *

·
*“Affine Cyclic Codes”, AMS Sectional Meeting,
University of Pittsburgh, Pittsburgh, PA November 2004.*

* *

·
*“A Generalization of Quasi-cyclic Codes”, AMS
Sectional Meeting, Special Session in Algebraic Coding Theory, Ohio
University, Athens, OH, March 2004.*

* *

·
*“On a Few Classes of Optimal and Near-Optimal
Polynomial Codes”, MTNS 2002, University of Notre Dame, South Bend,
IN, August 2002.*

* *

·
*“A Class of Near Optimal Polynomial
Codes”, Joint Mathematics Meetings, AMS Special Session in
Algebraic Coding Theory, San Diego, CA. January 2002.*

* *

·
*“A Family Polynomial Codes and a Class of
Griesmer Codes”, AMS Sectional Meeting, Special Session in Codes and
Designs, The Ohio State University, Columbus, OH. September 2001.*

* *

·
*“The Structure of 1-Generator Quasi-Twisted
Codes and New Linear Codes” XVth OSU-Dennison Conference, Special
Session in Combinatorics, The Ohio-State University, OH, May 2000.*

* *

·
*“Quaternary Quasi-Cyclic Codes and Some New
Binary Codes” AMS Sectional Meeting Notre Dame University, Special
Session in Algebraic Coding Theory, South Bend, IN. April 2000.*

* *

·
*“New Ternary Quasi-Cyclic Codes with Improved
Minimum Distances” AMS Sectional Meeting, University of Utah, Salt
Lake City, UT. September 1999.*

*Other Presentations*

·
*Delivered several talks on “Coding Theory”
and “The Legacy of Islamic Math and Science” in various places in
India in December 2023.*

·
*Numerous invited talks on “Coding Theory” and
“The Legacy of Islamic Math and Science” in various places in Algeria
and Morocco during my Fulbright stay in the AY 2022-23.*

·
*"Lessons from House of Wisdom and a Vision
for Future", A Revival of Islamic Academia Conference Memphis, TN,
July 2023*

·
*"Search for Good Linear Codes: The ASR
Algorithm and Its Generalizations", invited talk (remote), Algebra
with Applications Seminar, Aligarh Muslim University, India, May 2023.*

·
*“An Upper Level Math Course in Coding Theory
and Cryptography", Crypto Educators Seminar, virtual, April, 2023
(recording available) .*

·
*“A Mathematician's Journey into History of
Mathematics: Impacts, Reflections, and Lessons", invited national
talk, MAA Special Interest Group on History of Mathematics (HOM
SIGMAA), November 3, 2021 (recording available from the presenter).*

·
*“Islamic Art and Geometric Designs of
Mosques", presentation in the workshop titled **Exploring the Sacred in the Islamic Tradition**
organized by Spirituality Network, Columbus, OH November, 2019*

·
*"Research in Coding Theory: An
Efficient Way to Mathematical Fame and a Promise for the Quantum Age",
Colloquim Talk, New College of Florida, Sarasota, FL, March 2019.*

·
*“ The Legacy of Islamic Math and Science: Why
does it Matter in the 21st Century?", Colloquim Talk, New College of
Florida, Sarasota, FL, March 2019.*

·
*“ The Legacy of Islamic Math and Science: Why
does it Matter in the 21st Century?", **Mathematics Colloquim**, Northern
Arizona University, Flagstaff, AZ, March 2018.*

·
*“Recent Results in Quasi-Twisted and Related
Codes, and Codes over Rings", ACGT Seminar, Northern Arizona
University, Flagstaff, AZ, March 2018.*

·
*“Teaching a More Accurate and Inclusive
History of Science", (poster) Franklin University Scholars Showcase,
Columbus, OH, October 2018.*

·
*“The Legacy of Islamic Math and Science: A
Few Examples”, Oberlin College, Oberlin, OH, March 4, 2015.*

·
*“The Legacy of Islamic Math and Science: A
Few Examples”, University of Michigan-Dearborn, Dearborn, MI, March 3,
2015.*

* *

·
*“The Legacy of Islamic Science in the Modern
World: A Few Examples”, Rockford University, Rockford, IL, April 2014.*

* *

·
*“The Legacy of Islamic Mathematics and
Science: A Few Examples”, The College of Wooster, Wooster,November
2013.*

* *

·
*“Islam & Science: The Legacy of Islamic
Science in the Modern World, Noor Islamic Cultural and Community
Center, , Columbus, OH October 2013.*

* *

·
*“A Perfect Introduction to Coding Theory and
Search for Good Codes”, Oberlin College, Oberlin, OH, November 2008.*

* *

·
*“Some generalizations of cyclic codes:
Consta-cyclic, quasi-cyclic and quasi-twisted codes”, lecture given in
IMA Summer School, at University of Notre Dame, South Bend, IN, June
2004.*