Abstract
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.
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