Encoding via Gröbner bases and discrete Fourier transforms for several types of algebraic codes
arXiv:cs/0703104
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.
5 pages, 4 figures, To be presented at IEEE International Symposium on Information Theory 2007