Self-orthogonal codes over a non-unital ring from two class association schemes
Adel N. Alahmadi, Asmaa Melaibari, Patrick Solé · Journal of Algebra and Its Applications · 2023
There is a non-unital ring [Formula: see text] of order 4 defined by generators and relations as [Formula: see text] In this paper, we present special constructions of linear codes over [Formula: see text] 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 [Formula: see text] 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.