The build-up construction of quasi self-dual codes over a non-unital ring
Résumé
There is a local ring E of order 4, without identity for the multiplication , defined by generators and relations as E = a, b | 2a = 2b = 0, a 2 = a, b 2 = b, ab = a, ba = b. We study a recursive construction of self-orthogonal codes over E. We classify, up to permutation equivalence, self-orthogonal codes of length n and size 2 n (called here quasi self-dual codes or QSD) up to the length n = 12. In particular, we classify Type IV codes (QSD codes with even weights) up to n = 12.
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