On Coset Weight Distributions of the 3-Error-Correcting BCH-Codes

We study the coset weight distributions of the 3-error-correcting binary narrowsense BCH-codes and of their extensions, whose lengths are, respectively, 2m − 1 and 2m, m odd. We prove that all weight distributions are known as soon as those of the cosets of minimum weight 4 of the extended code are known. We point out that properties of the cosets which are orphans yield interesting properties on the other cosets. We describe the classes of cosets which are equivalent under the affine permutations. At the end we produce significant numerical results, proving that the number of distinct weight distributions of cosets increases with the length of the codes.