2006/09/29 by Maria Bras-Amorós, Bras-Amorós, Maria, Michael E. O’Sullivan +2
Computer Science · Engineering · Mathematics · #Coding theory and cryptography #Error Correcting Code Techniques #cs.DM #cs.IT #graph theory and CDMA systems #math.IT
paper · pdf · doi:10.48550/arxiv.cs/0609159
Added references
arxiv created 2006/12/11 · arxiv updated 2009/12/01
We consider generalizations of Reed-Muller codes, toric codes, and codes from certain plane curves, such as those defined by norm and trace functions on finite fields. In each case we are interested in codes defined by evaluating arbitrary subsets of monomials, and in identifying when the dual codes are also obtained by evaluating monomials. We then move to the context of order domain theory, in which the subsets of monomials can be chosen to optimize decoding performance using the Berlekamp-Massey-Sakata algorithm with majority voting. We show that for the codes under consideration these subsets are well-behaved and the dual codes are also defined by monomials.