Title :
Improving the upper bounds on the covering radii of Reed-Muller codes
Author :
Carlet, Claude ; Mesnager, Sihem
Author_Institution :
Projet CODES, INRIA, Le Chesnay
Abstract :
By deriving bounds on character sums of Boolean functions and by using the characterizations, due to Kasami and Tokura, of those elements of the Reed-Muller codes whose Hamming weights are smaller than twice 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
Keywords :
Boolean functions; Hamming codes; Reed-Muller codes; Boolean functions; Hamming weights; Reed-Muller codes; covering radii; Boolean functions; Cryptography; Error correction codes; Hamming weight; Maximum likelihood decoding; Upper bound;
Conference_Titel :
Information Theory, 2005. ISIT 2005. Proceedings. International Symposium on
Conference_Location :
Adelaide, SA
Print_ISBN :
0-7803-9151-9
DOI :
10.1109/ISIT.2005.1523446
