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

Nicola Pace, ,Chair of Operations Research - Technische Universität München, Arcisstr. 21, 80333 Munich, Germany, Angelo Sonnino, ,Dipartimento di Matematica, Informatica ed Economia - Università degli Studi della Basilicata, Viale dell'Ateneo Lucano, 10, 85100 Potenza, Italy
2019 Advances in Mathematics of Communications  
This paper deals with the problem of determining whether a PDset exists for a given linear code C and information set I. A computational approach is proposed and illustrated with two exceptional codes with automorphism groups isomorphic to the sporadic simple groups M 12 and M 22 , 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. 2010 Mathematics Subject Classification: Primary: 94B05, 94B35; Secondary: 20B25.
doi:10.3934/amc.2020065 fatcat:mxhxz5vzrfaqhbdmz7x2vnds4m