Encoding via Gröbner bases and discrete Fourier transforms for several types of algebraic codes

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dc.creatorMatsui, Hajime
dc.creatorMita, Seiichi
dc.date2007-03-22
dc.date2007-05-02
dc.date.accessioned2026-07-07T08:17:08Z
dc.date.available2026-07-07T08:17:08Z
dc.descriptionWe propose a novel encoding scheme for algebraic codes such as codes on algebraic curves, multidimensional cyclic codes, and hyperbolic cascaded Reed-Solomon codes and present numerical examples. We employ the recurrence from the Gröbner basis of the locator ideal for a set of rational points and the two-dimensional inverse discrete Fourier transform. We generalize the functioning of the generator polynomial for Reed-Solomon codes and develop systematic encoding for various algebraic codes.
dc.description5 pages, 4 figures, To be presented at IEEE International Symposium on Information Theory 2007
dc.identifierhttps://arxiv.org/abs/cs/0703104
dc.identifierhttp://arxiv.org/abs/cs/0703104
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/134022
dc.subjectInformation Theory
dc.titleEncoding via Gröbner bases and discrete Fourier transforms for several types of algebraic codes
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