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. The necessary tools are already incorporated in SYMMETRICA, a (public domain) 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.
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© 1995 Springer-Verlag Berlin Heidelberg
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Fripertinger, H., Kerber, A. (1995). Isometry classes of indecomposable linear codes. In: Cohen, G., Giusti, M., Mora, T. (eds) Applied Algebra, Algebraic Algorithms and Error-Correcting Codes. AAECC 1995. Lecture Notes in Computer Science, vol 948. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60114-7_15
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DOI: https://doi.org/10.1007/3-540-60114-7_15
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