A note on the binary codes from triangular graphs - Rodrigues B.G. (Utilitas Mathematica, 2008)
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 An acts as an automorphism group of C we determine (An)w, for either choices of the weight of w and show that (An)w is a maximal subgroup of An.