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A Geometrical Realisation of Quasi-Cyclic Codes

In: Probability, Combinatorics and Control

Author

Listed:
  • Cristina Martinez Ramirez
  • Alberto Besana

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.

Suggested Citation

  • Cristina Martinez Ramirez & Alberto Besana, 2020. "A Geometrical Realisation of Quasi-Cyclic Codes," Chapters, in: Andrey Kostogryzov & Victor Korolev (ed.), Probability, Combinatorics and Control, IntechOpen.
    • Handle: RePEc:ito:pchaps:197823
    DOI: 10.5772/intechopen.88288
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    More about this item

    Keywords

    cyclic code; partition; Grassmannian;
    All these keywords.

    JEL classification:

    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General

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