2007/03/22 by Hajime Matsui, Matsui, Hajime, Seiichi Mita +1
Computer Science · Mathematics · #Coding theory and cryptography #Cryptographic Implementations and Security #Cryptography and Residue Arithmetic #cs.IT #math.IT
paper · pdf · doi:10.48550/arxiv.cs/0703104
5 pages, 4 figures, To be presented at IEEE International Symposium on Information Theory 2007
arxiv created 2007/05/02 · arxiv updated 2009/12/01
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.