Cyclic Codes over a Non-Local Non-Unital Ring

Autor:	Adel Alahmadi, Malak Altaiary, Patrick Solé
Jazyk:	angličtina
Rok vydání:	2024
Předmět:	non-unitary rings cyclic codes self-orthogonal codes Mathematics QA1-939
Zdroj:	Mathematics, Vol 12, Iss 6, p 866 (2024)
Druh dokumentu:	article
ISSN:	2227-7390
DOI:	10.3390/math12060866
Popis:	We study cyclic codes over the ring H of order 4 and characteristic 2 defined by generators and relations as H=⟨a,b∣2a=2b=0,a2=0,b2=b,ab=ba=0⟩. This is the first time that cyclic codes over a non-unitary ring are studied. Every cyclic code of length n over H is uniquely determined by the data of an ordered pair of binary cyclic codes of length n. We characterize self-dual, quasi-self-dual, and linear complementary dual cyclic codes H. We classify cyclic codes of length at most 7 up to equivalence. A Gray map between cyclic codes of length n over H and quasi-cyclic codes of length 2n over F2 is studied.
Databáze:	Directory of Open Access Journals
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