PD-sets for codes related to flag-transitive symmetric designs

‎For any prime p let C_p(G) be the p-ary code spanned by the rows of the incidence matrix G of a graph \Gamma‎. ‎Let \Gamma be the incidence graph of a flag-transitive symmetric design D‎. ‎We show that any flag-transitive‎ ‎automorphism group of D can be used as a PD-set for full error correction for the linear code C_p(G)‎ ‎(with any information set)‎. ‎It follows that such codes derived from flag-transitive symmetric designs can be‎ ‎decoded using permutation decoding‎. ‎In that way to each flag-transitive symmetric (v‎, ‎k‎, ‎\lambda) design we associate a linear code of length vk that is‎ ‎permutation decodable‎. ‎PD-sets obtained in the described way are usually of large cardinality‎. ‎By studying codes arising from some flag-transitive symmetric designs we show that smaller PD-sets can be found for‎ ‎specific information sets‎.

Keywords:

Code , graph , flag-transitive design , permutation decoding