University of Isfahan Transactions on Combinatorics 2251-8657 7 1 2018 03 01 PD-sets for codes related to flag-transitive symmetric designs 37 50 21615 10.22108/toc.2017.21615 EN Dean Crnkovic Department of Mathematics, University of Rijeka, Radmile Matječić 2, 51000 Rijeka, Croatia Nina Mostarac Department of Mathematics, University of Rijeka, Rijeka, Croatia Journal Article 2017 06 04 ‎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. https://toc.ui.ac.ir/article_21615_538caf5ff8ba2437eee5ab750d6dce2a.pdf