Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5776954 | Discrete Mathematics | 2017 | 7 Pages |
Abstract
It is shown that for nâ¥5 and râ¤nâ12, 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 1â¤sâ¤Mâ1, 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), s-PD-sets of size s+1 are constructed for s up to the bound â2nn+1ââ1. The results apply also to generalized Reed-Muller codes.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
J.D. Key, T.P. McDonough, V.C. Mavron,