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:
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
Coding Theory and Cryptography
· 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, accepted for publication in Cryptography and Communications.
· 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), accepted for publication in JACODESMATH
· Z. Hebbache, A. Kaya, N. Aydin, K. Guenda, On Some Skew Codes over Zq+uZq, accepted for publication in Discrete Mathematics, Algorithms, and Application, 2022.
· 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.
· 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, 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
· 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,
N. Aydin, J. Murphree*
S. Karadeniz, B. Yildiz and N. Aydin,
T. Abualrub, I. Siap and N. Aydin,
N. Aydin, S.
Karadeniz, and B. Yildiz,
T. Abualrub, N.
Aydin, and P. Seneviratne,
I. Siap, T.
Abualrub, N. Aydin, and P. Seneviratne,
I. Siap, T.
Abualrub and N. Aydin
N. Aydin, and
T. A. Gulliver,
R. Ackerman*, and N. Aydin,
T. Abualrub, A. Ghrayeb,
N. Aydin, T. Asamov*,
· 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.
· T. Asamov*, and N. Aydin, “LDPC codes of arbitrary girth”, In Proceedings of the 10th 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.
I. Siap, N. Aydin
and D. Ray-Chaudhuri “New 1-generator quasi-twisted codes
over GF(5)” In Codes and
(Piscataway, NJ, 1999),
pp. 265-275, DIMACS
Ser. Discrete Math. & Theor. Comp. Sci., AMS.,
· 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 Role of Religion in the Development of Mathematical Sciences in Medieval Islamic Civilization", Muslim Heritage, 2021.
• 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.
• 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
• 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.
· “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.
and Mathematical Sciences”, Online
in Skew Cyclic Codes”, 31st
Ohio State-Denison Mathematics Conference,
Cyclic Codes", ICAAA
2011, International Conference on Applied Analysis and
· “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,
“Search for Good
Linear Codes over Z_4 and a New Database”, International
Conference on Algebra and its Applications,
“Search for Good
Linear Codes”, 29th OSU-Denison Conference, Special
Session in Combinatorics, The
problems on quasi-twisted and related code constructions
and good quaternary codes”, International Symposium on
· “Enhancing undergraduate mathematics curriculum via coding theory and cryptography”, Poster presentation, in 3rd 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.
Codes”, AMS Sectional Meeting,
· “A Generalization of Quasi-cyclic Codes”, AMS Sectional Meeting, Special Session in Algebraic Coding Theory, Ohio University, Athens, OH, March 2004.
a Few Classes of Optimal and Near-Optimal Polynomial
Codes”, MTNS 2002,
· “A Class of Near Optimal Polynomial Codes”, Joint Mathematics Meetings, AMS Special Session in Algebraic Coding Theory, San Diego, CA. January 2002.
Polynomial Codes and a Class of Griesmer Codes”, AMS
Sectional Meeting, Special Session in Codes and Designs,
· “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.
Quasi-Cyclic Codes and Some New Binary Codes”
Quasi-Cyclic Codes with Improved Minimum Distances”
AMS Sectional Meeting,
· “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,
“The Legacy of
Islamic Math and Science: A Few Examples”, University of
Michigan-Dearborn, Dearborn, MI,
“The Legacy of
Islamic Science in the Modern World: A Few Examples”,
Rockford University, Rockford, IL,
Science: The Legacy of Islamic Science in the Modern
World, Noor Islamic Cultural and Community Center,
Introduction to Coding Theory and Search for Good Codes”,
Oberlin College, Oberlin, OH,
· “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.