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- Title
Mass Formula for Self-Orthogonal and Self-Dual Codes over Non-Unital Rings of Order Four.
- Authors
Alahmadi, Adel; Alshuhail, Altaf; Betty, Rowena Alma; Galvez, Lucky; Solé, Patrick
- Abstract
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 | 2 a = 2 b = 0 , a 2 = b , ab = 0 and the noncommutative ring E = a , b | 2 a = 2 b = 0 , a 2 = a , b 2 = 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.
- Subjects
NONCOMMUTATIVE rings; COMMUTATIVE rings
- Publication
Mathematics (2227-7390), 2023, Vol 11, Issue 23, p4736
- ISSN
2227-7390
- Publication type
Article
- DOI
10.3390/math11234736