Discrete Mathematics in Coding Theory

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Mathematics and Computer Science".

Deadline for manuscript submissions: 25 May 2025 | Viewed by 403

Special Issue Editor


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Guest Editor
I2M, CNRS, Aix-Marseille University, Centrale Marseille, Marseilles, France
Interests: discrete mathematics; cryptography coding; information theory; mathematical analysis; communication science; geometry; topology; algorithms; pure mathematics
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Special Issue Information

Dear Colleagues,

Discrete mathematics, as opposed to continuous mathematics, comprises, broadly speaking, algebra, combinatorics, probability, and number theory.

The history of the domain shows that all these fields in turn have contributed to coding theory. Therefore, they can all contribute to this Special Issue. More specifically, we welcome the submission of original papers in the following areas (the list is not exhaustive):

  • Codes and finite geometry: space time codes, rank metric codes, AG codes; Boolean functions.
  • Codes and group theory: association schemes, modular representation; completely regular codes.
  • Codes and Number Theory: global codes, Gauss sums, Jacobi sums; exponential sums for explicit enumeration.
  • Codes and combinatorics: block designs, maximal codes, few weights codes; Hadamard matrices.
  • Algebraic coding theory: codes over rings and modules, codes as ideals and modules over rings.
  • Algorithms for effective construction and efficient decoding; cryptographical protocols. 

Prof. Dr. Patrick Solé
Guest Editor

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Keywords

  • codes
  • designs
  • rings
  • modules
  • graphs
  • discrete algorithms
  • incidence geometry
  • arithmetic geometry

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Published Papers (1 paper)

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Research

18 pages, 342 KiB  
Article
Linear Codes and Self-Polarity
by Iliya Bouyukliev, Stefka Bouyuklieva, Mariya Dzhumalieva-Stoeva and Dushan Bikov
Mathematics 2024, 12(22), 3555; https://doi.org/10.3390/math12223555 - 14 Nov 2024
Viewed by 261
Abstract
This work studies projective self-dual (PSD) and self-polar linear codes over finite fields with q elements, where q is a power of a prime. The possible parameters for which PSD codes may exist are presented, and many examples are provided. Algorithms for checking [...] Read more.
This work studies projective self-dual (PSD) and self-polar linear codes over finite fields with q elements, where q is a power of a prime. The possible parameters for which PSD codes may exist are presented, and many examples are provided. Algorithms for checking whether a q-ary linear code is self-polar are described. Many PSD and self-polar codes over fields with two, three, four, and five elements with two and three nonzero weights are constructed. Full article
(This article belongs to the Special Issue Discrete Mathematics in Coding Theory)
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