The build-up construction of quasi self-dual codes over a non-unital ring

There is a local ring E of order 4, without identity for the multiplication, defined by generators and relations as E = < a, b vertical bar 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.

Automated summary

This research explores the recursive construction of self-orthogonal codes over a local ring E without an identity for multiplication. It classifies self-orthogonal codes of length n and size 2(n) (referred to as quasi self-dual codes or QSD) up to n = 12, up to permutation equivalence. In particular, it focuses on classifying Type IV codes (even-weight QSD codes) up to n = 12.