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 flagtransitive symmetric design $D$‎. ‎We show that any flagtransitive‎ ‎automorphism group of $D$ can be used as a PDset for full error correction for the linear code $C_p(G)$‎ ‎(with any information set)‎. ‎It follows that such codes derived from flagtransitive symmetric designs can be‎ ‎decoded using permutation decoding‎. ‎In that way to each flagtransitive symmetric $(v‎, ‎k‎, ‎lambda)$ design we associate a linear code of length $vk$ that is‎ ‎permutation decodable‎. ‎PDsets obtained in the described way are usually of large cardinality‎. ‎By studying codes arising from some flagtransitive symmetric designs we show that smaller PDsets can be found for‎ ‎specific information sets‎.