An asymptotic bound on the covering radii of binary BCH codes

Abstract

P. Deligne's theorem (1974) is used to prove that the covering radius of a primitive binary BCH code with designed distance 2t+1 is equal to 2t-1 if t is of the form 2/sup u/+1 and the code length is at least (2t)/sup 4t-2/. It is believed that this is the first time Deligne's theorem is used on coding theory.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>