Abstract
There is a local ring I of order 4, without identity for the multiplication, defined by generators and relations as
I = < a, b vertical bar 2a = 2b = 0, a(2 )= b, ab = 0 >.
We study a recursive construction of self-orthogonal codes over I. We classify self orthogonal codes of length n and size 2(n) (called here quasi self-dual codes or QSD) up to the length n = 6. In particular, we classify Type IV codes (QSD codes with even weights) and quasi Type IV codes (QSD codes with even torsion code) up to n = 6.