1. Self-orthogonal codes over a non-unital ring and combinatorial matrices.
- Author
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Shi, Minjia, Wang, Shukai, Kim, Jon-Lark, and Solé, Patrick
- Subjects
MATRIX rings ,LOCAL rings (Algebra) ,REGULAR graphs ,HAMMING weight ,MULTIPLICATION - Abstract
There is a local ring E of order 4, without identity for the multiplication, defined by generators and relations as E = ⟨ a , b ∣ 2 a = 2 b = 0 , a 2 = a , b 2 = b , a b = a , b a = b ⟩. We study a special construction of self-orthogonal codes over E, based on combinatorial matrices related to two-class association schemes, Strongly Regular Graphs (SRG), and Doubly Regular Tournaments (DRT). We construct quasi self-dual codes over E, and Type IV codes, that is, quasi self-dual codes whose codewords all have even Hamming weight. All these codes can be represented as formally self-dual additive codes over F 4. The classical invariant theory bound for the weight enumerators of this class of codes improves the known bound on the minimum distance of Type IV codes over E. [ABSTRACT FROM AUTHOR]
- Published
- 2023
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