Sign in to use this feature.

Years

Between: -

Subjects

remove_circle_outline
remove_circle_outline
remove_circle_outline

Journals

Article Types

Countries / Regions

Search Results (2)

Search Parameters:
Keywords = left self-dual codes

Order results
Result details
Results per page
Select all
Export citation of selected articles as:
17 pages, 287 KB  
Article
Cyclic Codes over a Non-Commutative Non-Unital Ring
by Adel Alahmadi, Malak Altaiary and Patrick Solé
Mathematics 2024, 12(13), 2014; https://doi.org/10.3390/math12132014 - 28 Jun 2024
Cited by 1 | Viewed by 912
Abstract
In this paper, we investigate cyclic codes over the ring E of order 4 and characteristic 2 defined by generators and relations as [...] Read more.
In this paper, we investigate cyclic codes over the ring E of order 4 and characteristic 2 defined by generators and relations as E=a,b2a=2b=0,a2=a,b2=b,ab=a,ba=b. This is the first time that cyclic codes over the ring E are studied. Each cyclic code of length n over E is identified uniquely by the data of an ordered pair of binary cyclic codes of length n. We characterize self-dual, left self-dual, right self-dual, and linear complementary dual (LCD) cyclic codes over E. We classify cyclic codes of length at most 7 up to equivalence. A Gray map between cyclic codes of length n over E and quasi-cyclic codes of length 2n over F2 is studied. Motivated by DNA computing, conditions for reversibility and invariance under complementation are derived. Full article
11 pages, 293 KB  
Article
The Mass Formula for Self-Orthogonal and Self-Dual Codes over a Non-Unitary Non-Commutative Ring
by Adel Alahmadi, Altaf Alshuhail, Rowena Alma Betty, Lucky Galvez and Patrick Solé
Mathematics 2024, 12(6), 862; https://doi.org/10.3390/math12060862 - 15 Mar 2024
Cited by 2 | Viewed by 1414
Abstract
In this paper, we derive a mass formula for the self-orthogonal codes and self-dual codes over a non-commutative non-unitary ring, namely, [...] Read more.
In this paper, we derive a mass formula for the self-orthogonal codes and self-dual codes over a non-commutative non-unitary ring, namely, Ep=a,b|pa=pb=0,a2=a,b2=b,ab=a,ba=b, where ab and p is any odd prime. We also give a classification of self-orthogonal codes and self-dual codes over Ep, where p=3,5, and 7, in short lengths. Full article
(This article belongs to the Section A: Algebra and Logic)
Back to TopTop