A note on the binary codes from triangular graphs

Abstract

For a codeword w of weight i where i = 4(n - 4) or i = 2(n - 2) depending on whether n ≥ 10 and even or n ≥ 5 and odd, from the binary code C obtained from an adjacency matrix of the triangular graph T(n) for any n ≥ 5, we determine the stabilizer Aut(C)_w in Aut(C) and show that Aut(C)_w is a maximal subgroup of Aut(C). Furthermore, since the alternating group A_n acts as an automorphism group of C we determine (A_n)_w, for either choices of the weight of w and show that (A_n)_w is a maximal subgroup of A_n.