A Lower Bound on the Optimum Distance Profiles of the Second-Order Reed-Muller Codes

作者：Chen Yanling^*; Vinck A J Han

来源：IEEE Transactions on Information Theory, 2010, 56(9): 4309-4320.

DOI：10.1109/TIT.2010.2054512

• Boolean function
• MacWilliams' identities
• optimum distance profile
• Reed-Muller code
• symplectic matrix

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.

• 出版日期2010-9