The build-up construction of quasi self-dual codes over a non-unital ring. (English) Zbl 1495.94098
Summary: There is a local ring \(E\) of order \(4,\) without identity for the multiplication, defined by generators and relations as
\[
E=\langle a,b\,|\,2a=2b=0, a^2=a, b^2=b,ab=a,ba=b\rangle.
\] 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 \(n=12\).
MSC:
| 94B05 | Linear codes (general theory) |
| 16L30 | Noncommutative local and semilocal rings, perfect rings |
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