ON COSETS OF WEIGHT 4 OF BCH(2~m,8), m EVEN, AND EXPONENTIAL SUMS

摘要

We give exact expressions for the number of coset leaders in the cosets of weight 4 of binary primitive narrow sense Bose-Chaudury-Hocquenghem (BCH) codes of length n = 2~m (m even) with minimum distance 8 in terms of several exponential sums, including cubic sums and Kloosterman sums. This allows us to bound the number of coset leaders in these cosets.