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Mathematics
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Advances in Contemporary Coding Theory
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Advances in Contemporary Coding Theory

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Algebra, Geometry and Topology".

Deadline for manuscript submissions: closed (31 March 2022) | Viewed by 3413

Special Issue Editor

Prof. Dr. Patrick Solé

E-Mail Website
Guest Editor
I2M, CNRS, Aix-Marseille University, Centrale Marseille, Marseilles, France
Interests: coding theory; algebraic combinatorics; number theory
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

We are seeking papers on Mathematical Coding Theory, both pure and applied. Algebraic topics like cyclic codes and their generalizations over fields and rings are welcome. Combinatorial topics like completely regular codes, codes on posets, and self-dual codes are also welcome.

Prof. Dr. Patrick Solé
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • codes over rings
  • exact weight enumeration
  • asymptotic performance
  • code-based cryptography

Published Papers (2 papers)

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Research

14 pages, 318 KiB  
Article
Extremal Binary and Ternary Codes of Length 60 with an Automorphism of Order 29 and a Generalization
by Stefka Bouyuklieva, Javier de la Cruz and Darwin Villar
Mathematics 2022, 10(5), 748; https://doi.org/10.3390/math10050748 - 26 Feb 2022
Cited by 2 | Viewed by 1040
Abstract
In this paper, all extremal Type I and Type III codes of length 60 with an automorphism of order 29 are classified up to equivalence. In both cases, it has been proven that there are three inequivalent codes. In addition, a new family [...] Read more.
In this paper, all extremal Type I and Type III codes of length 60 with an automorphism of order 29 are classified up to equivalence. In both cases, it has been proven that there are three inequivalent codes. In addition, a new family of self-dual codes over non-binary fields is presented. Full article
(This article belongs to the Special Issue Advances in Contemporary Coding Theory)
19 pages, 357 KiB  
Article
On the State Approach Representations of Convolutional Codes over Rings of Modular Integers
by Ángel Luis Muñoz Castañeda, Noemí DeCastro-García and Miguel V. Carriegos
Mathematics 2021, 9(22), 2962; https://doi.org/10.3390/math9222962 - 20 Nov 2021
Cited by 1 | Viewed by 1513
Abstract
In this study, we prove the existence of minimal first-order representations for convolutional codes with the predictable degree property over principal ideal artinian rings. Further, we prove that any such first-order representation leads to an input/state/output representation of the code provided the base [...] Read more.
In this study, we prove the existence of minimal first-order representations for convolutional codes with the predictable degree property over principal ideal artinian rings. Further, we prove that any such first-order representation leads to an input/state/output representation of the code provided the base ring is local. When the base ring is a finite field, we recover the classical construction, studied in depth by J. Rosenthal and E. V. York. This allows us to construct observable convolutional codes over such rings in the same way as is carried out in classical convolutional coding theory. Furthermore, we prove the minimality of the obtained representations. This completes the study of the existence of input/state/output representations of convolutional codes over rings of modular integers. Full article
(This article belongs to the Special Issue Advances in Contemporary Coding Theory)
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