SELF-ORTHOGONAL CODES OVER A NON-UNITAL RINGFROM TWO CLASS ASSOCIATION SCHEMES
Résumé
There is a non-unital ring I of order 4 defined by generators and relations as I = a, b | 2a = 2b = 0, a 2 = b, ab = 0. In this paper, we present special constructions of linear codes over I from the adjacency matrices of two class association schemes. These consist of either Strongly Regular Graphs (SRGs) or Doubly Regular Tournaments (DRTs). We investigate the conditions under which these codes are self-orthogonal, quasi self-dual, or Type IV. As a byproduct of this study, some diophantine relations on the weight of sum of vectors with coefficients in I are derived. Some examples of codes with minimum distance better than that of Type IV codes over unital rings of the same order in modest lengths are given.
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