Mass Formula for Self-Orthogonal and Self-Dual Codes over Non-Unital Rings of Order Four

Autor:	Adel Alahmadi, Altaf Alshuhail, Rowena Alma Betty, Lucky Galvez, Patrick Solé
Jazyk:	angličtina
Rok vydání:	2023
Předmět:	code over ring non-unital ring self-orthogonal code quasi self-dual self-dual code mass formulas Mathematics QA1-939
Zdroj:	Mathematics, Vol 11, Iss 23, p 4736 (2023)
Druh dokumentu:	article
ISSN:	2227-7390
DOI:	10.3390/math11234736
Popis:	We study the structure of self-orthogonal and self-dual codes over two non-unital rings of order four, namely, the commutative ring I=a,b|2a=2b=0,a2=b,ab=0 and the noncommutative ring E=a,b|2a=2b=0,a2=a,b2=b,ab=a,ba=b. We use these structures to give mass formulas for self-orthogonal and self-dual codes over these two rings, that is, we give the formulas for the number of inequivalent self-orthogonal and self-dual codes, of a given type, over the said rings. Finally, using the mass formulas, we classify self-orthogonal and self-dual codes over each ring, for small lengths and types.
Databáze:	Directory of Open Access Journals
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