Permutation decoding for the binary codes from triangular graphs. (Q1422399)

Permutation decoding is an algorithm for decoding linear codes introduced by \textit{F. J. MacWilliams} [Bell Syst. Tech. J. 43, 485--505 (1964; Zbl 0116.35304)] that uses certain sets (called PD-sets) of permutations in the automorphism group of the code. The paper investigates PD-sets for the binary linear codes spanned by the rows of the adjacency matrix of a triangular graph \(T(n)\), having as vertices the 2-element subsets of a given set of size \(n\). Explicit PD-sets are found for every \(n\geq 5\).