Improved partial permutation decoding for Reed-Muller codes

被引：8
|
作者：
Key, J. D. [1 ]
McDonough, T. P. [1 ]
Mavron, V. C. [1 ]
机构：
[1] Aberystwyth Univ, Inst Math Phys & Comp Sci, Aberystwyth SY23 3BZ, Dyfed, Wales
来源：
DISCRETE MATHEMATICS | 2017年 / 340卷 / 04期
关键词：
Reed-Muller codes; Permutation decoding; SETS;
D O I：
10.1016/j.disc.2016.11.031
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
It is shown that for n >= 5 and r <= n-1/2, if an (n, M, 2r + 1) binary code exists, then the rth-order Reed-Muller code R(r n) has s-PD-sets of the minimum size s + 1 for 1 <= s <= M - 1, and these PD-sets correspond to sets of translations of the vector space F-2(n). In addition, for the first order Reed-Muller code R(1, n), s-PD-sets of size s+1 are constructed for sup to the bound [2(n)/n+1] - 1. The results apply also to generalized Reed-Muller codes. (C) 2016 Elsevier B.V. All rights reserved.
引用
收藏
页码：722 / 728
页数：7
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