THE BUILD-UP CONSTRUCTION OVER A COMMUTATIVE NON-UNITAL RING

There is a local ring I of order 4, without identity for the multiplication , defined by generators and relations as I = a, b | 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 (i.e. QSD codes with even weights) and quasi Type IV codes (i.e. QSD codes with even torsion code) up to n = 6. 2010 Mathematics Subject Classification. Primary: 49B05; Secondary: 16A10