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

Hajime Matsui·Seiichi Mita
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Abstract

We 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.

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Hajime Matsui, Seiichi Mita. 2007-05-02. Encoding via Gröbner bases and discrete Fourier transforms for several types of algebraic codes. https://arxiv.org/abs/cs/0703104

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