The weight distribution of hulls of binary codes from incidence matrices of complete graphs

Abstract

We characterise the weights of all codewords of the hull of the binary code spanned by rows of an incidence matrix B_n of the complete graph K_n for n ≥ 4 and n even. Among others, we show that every codeword of the hull is the sum of an even number of rows of B_n and that its weight depends on the number of rows required to span it. We also determine the weight enumerator and the MacWilliams identity for the hull.