Enumeration of isometry classes of linear (n,k) -codes over GF(q) in SYMMETRICA Publications, to be read Cycle indices of linear, affine and projective groups Isometry Classes of Indecomposable Linear Codes

Isometry Classes of Indecomposable Linear Codes

Jointly written with ADALBERT KERBER. Lecture Notes in Computer Science 948, Proceedings of Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, 11th International Symposium, AAECC-11, Paris, France, July 1995, (G. Cohen, M. Giusti, and T. Mora editors), 194 - 204, 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.


harald.fripertinger "at" uni-graz.at, October 12, 2017

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