A Geometrical Realisation of Quasi-Cyclic Codes

Cristina Martinez Ramirez and Alberto Besana

A chapter in Probability, Combinatorics and Control from IntechOpen

Abstract: We study and enumerate cyclic codes which include generalised Reed-Solomon codes as function field codes. This geometrical approach allows to construct longer codes and to get more information on the parameters defining the codes. We provide a closed formula in terms of Stirling numbers for the number of irreducible polynomials and we relate it with other formulas existing in the literature. Further, we study quasi-cyclic codes as orbit codes in the Grassmannian parameterizing constant dimension codes. In addition, we review Horn's algorithm and apply it to construct classical codes by their defining ideals.

Keywords: cyclic code; partition; Grassmannian (search for similar items in EconPapers)
JEL-codes: C60 (search for similar items in EconPapers)
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Persistent link: https://EconPapers.repec.org/RePEc:ito:pchaps:197823

DOI: 10.5772/intechopen.88288

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