Partial permutation decoding for codes from affine geometry designs (Q2482314)

Permutation decoding (PD) was first introduced and developed by MacWilliams. This method is fully described in the classical text on coding theory by MacWilliams and Sloane. This concept was extended to that of an \(s-PD\)-set for \(s\)-error correction by the authors in an earlier paper [European J. Combin. 26, No.~5, 665--682 (2005; Zbl 1074.94014)]. The definition of a \(PD\)-set depends on the automorphism group of the code and and \(s-PD\)-set can also correct upto \(s\) errors. In an earlier paper by the authors [Finite Fields Appl. 12, 232--247 (2006; Zbl 1089.94044)], information sets in codes were found. The present paper uses these information sets on the code of the affine space \(AG_3({\mathbb{F}}_p)\) where \(p\) is a prime to construct \(PD\)-sets for a large class of codes.