On the existence of pd-sets: Algorithms arising from automorphism groups of codes

This paper deals with the problem of determining whether a PD-set exists for a given linear code C and information set I. A computational approach is proposed and illustrated with two exceptional codes with auto-morphism groups isomorphic to the sporadic simple groups M12 and M22, respectively. In both cases, the existence of a PD–set is proven. In general, the algorithm works well whenever the code C has a very large automorphism group.