Isometry Classes of Indecomposable Linear Codes

Harald Fripertinger, Adalbert Kerber

January 30, 1995

Abstract

In the constructive theory of linear codes, we can restrict attention to the isometry classes of indecomposable codes, as it was shown by Slepian. We describe these classes as orbits and we demonstrate how they can be enumerated using cycle index polynomials and the tools already incorporated in SYMMETRICA, a computer algebra package devoted to representation theory and combinatorics of symmetric groups and of related classes of groups. Moreover, we describe how systems of representatives of these classes can be evaluated using double coset methods.