Binary codes from designs from the reflexive n-cube

Abstract

We show that the binary code obtained from the row span over F2 of a matrix A_n + I_2n where A_n is an adjacency matrix for the n-cube (i.e. the Hamming graph H(n,2)) is self-dual if n is odd and can be used for partial permutation decoding. The automorphism group for the neighbourhood design is shown to be larger than that for the n-cube for n > 2, and equal to that of the code in the case of odd n > 5. Taken together with the binary codes fromthe n-cube, this provides a class of self-dual codes of length 2_n for all n > 5 thatcan be used for partial permutation decoding.