TY - JOUR
T1 - Reed-Muller codes and permutation decoding
AU - Key, Jennifer D.
AU - McDonough, Thomas
AU - Mavron, Vassili C.
N1 - Mavron, V. C., Key, J. D., McDonough, T. P. (2010) Reed-Muller codes and permutation decoding. Discrete Mathematics, 310 (22), 3114-3119
Sponsorship: London Mathematical Society (Partial support)
PY - 2010/11/28
Y1 - 2010/11/28
N2 - We show that the first- and second-order Reed–Muller codes, and , can be used for permutation decoding by finding, within the translation group, (m−1)- and (m+1)-PD-sets for for m≥5,6, respectively, and (m−3)-PD-sets for for m≥8. We extend the results of Seneviratne [P. Seneviratne, Partial permutation decoding for the first-order Reed-Muller codes, Discrete Math., 309 (2009), 1967–1970].
AB - We show that the first- and second-order Reed–Muller codes, and , can be used for permutation decoding by finding, within the translation group, (m−1)- and (m+1)-PD-sets for for m≥5,6, respectively, and (m−3)-PD-sets for for m≥8. We extend the results of Seneviratne [P. Seneviratne, Partial permutation decoding for the first-order Reed-Muller codes, Discrete Math., 309 (2009), 1967–1970].
U2 - 10.1016/j.disc.2009.06.001
DO - 10.1016/j.disc.2009.06.001
M3 - Article
SP - 3114
EP - 3119
JO - Discrete Mathematics
JF - Discrete Mathematics
ER -