Title :
A Lower Bound on the Optimum Distance Profiles of the Second-Order Reed–Muller Codes
Author :
Chen, Yanling ; Vinck, A. J Han
Author_Institution :
Fraunhofer IESE, Kaiserslautern, Germany
Abstract :
In this paper, we give a lower bound for the optimum distance profiles of the second-order Reed-Muller code in the dictionary order and in the inverse dictionary order. In particular, we investigate the second-order Reed-Muller codes of length ≤ 256. We show that the bound is tight in both orders for the codes of length ≤ 128 .
Keywords :
Reed-Muller codes; matrix algebra; inverse dictionary order; lower bound; optimum distance profiles; second-order reed-muller codes; symplectic matrix; Block codes; Boolean functions; Channel coding; Decoding; Dictionaries; Distance measurement; Error correction; Error correction codes; Generators; Linear code; Mathematics; Polarization; Upper bound; Boolean function; MacWilliams´ identities; Reed–Muller code; optimum distance profile; symplectic matrix;
Journal_Title :
Information Theory, IEEE Transactions on
DOI :
10.1109/TIT.2010.2054512
