On the stabilizers of the minimum-weight codewords of some binary codes from graphs on triples

Abstract

We determine the stabilizers of the minimum-weight codewords for the binary codes C ₂(n) and C ₂(n)^⊥ obtained from an adjacency matrix of the graph A ₂(n) for n ≥ 7 and odd, with vertex set Ω^{3}, and adjacency defined by two vertices as 3-sets being adjacent if they have two elements in common. In addition we show that the stabilizers of the minimum-weight codewords of these binary codes are maximal subgroups of the automorphisms groups of the codes.