Improved partial permutation decoding for Reed-Muller codes

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• 作者：J.D. Key ^{keyj@clemson.edu} ; T.P. McDonough ; V.C. Mavron
• 关键词：Reed&ndash ; Muller codes ; Permutation decoding
• 刊名：Discrete Mathematics
• 出版年：2017
• 出版时间：April 2017
• 年：2017
• 卷：340
• 期：4
• 页码：722-728
• 全文大小：461 K
• 卷排序：340

文摘

It is shown that for n≥5n≥5 and r≤n−12, if an (n,M,2r+1)(n,M,2r+1) binary code exists, then the rrth-order Reed–Muller code R(r,n)R(r,n) has ss-PD-sets of the minimum size s+1s+1 for 1≤s≤M−11≤s≤M−1, and these PD-sets correspond to sets of translations of the vector space F2n. In addition, for the first order Reed–Muller code R(1,n)R(1,n), ss-PD-sets of size s+1s+1 are constructed for ss up to the bound ⌊2nn+1⌋−1. The results apply also to generalized Reed–Muller codes.