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Improving the Upper Bounds on the Covering Radii of Binary Reed–Muller Codes

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2 Author(s)
Claude Carlet ; Projet CODES, INRIA, Le Chesnay ; Sihem Mesnager

By deriving bounds on character sums of Boolean functions and by using the characterizations, due to Kasami , of those elements of the Reed-Muller codes whose Hamming weights are smaller than twice and a half the minimum distance, we derive an improved upper bound on the covering radius of the Reed-Muller code of order 2, and we deduce improved upper bounds on the covering radii of the Reed-Muller codes of higher orders

Published in:

IEEE Transactions on Information Theory  (Volume:53 ,  Issue: 1 )