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

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

2007-03-22

arxiv.org/abs/cs/0703104v2

Computer Science

Information Theory

5 pages, 4 figures, To be presented at IEEE International Symposium on Information Theory 2007

Scientific paper

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 Gr\"obner 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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