Codes from multipartite graphs and minimal permutation decoding sets

Permutation decoding method developed by MacWilliams and described in [Permutation decoding of systematic codes, Bell Syst. Tech. J. 43 (1964) 485-505] is a decoding technique that uses a subset of the automorphism group of the code called a PD-set. The complexity of the permutation decoding algorithm depends on the size of the PD-set and finding a minimal PD-set for an error correcting code is a hard problem. In this paper we examine binary codes from the complete-multipartite graph Gamma = Kn(1),..., n(m) and find PD-sets for all values of m and n(i). Further we show that these PD-sets are minimal when m is odd and n(1) = n(2) = center dot center dot center dot = n(m).