Title :
Improving the Upper Bounds on the Covering Radii of Binary 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 , 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
Keywords :
Boolean functions; Hamming codes; Reed-Muller codes; binary codes; Boolean functions; Hamming weights; binary Reed-Muller codes; covering radius; upper bound; Australia; Boolean functions; Cryptography; Error correction codes; Hamming weight; Information theory; Maximum likelihood decoding; Measurement standards; Polynomials; Upper bound; Character sum; Reed–Muller codes; covering radius;
Journal_Title :
Information Theory, IEEE Transactions on
DOI :
10.1109/TIT.2006.887494
