Weight distributions of cosets of two-error-correcting binary BCH codes, extended or not

Let B be the binary two-error-correcting BCH code of length 2" 1 and let B be the extended code of B. We give formal expressions of weight distributions of the cosets of the codes B only depending on m. We can then deduce the weight distributions of the cosets of B. When m is odd, it is well known that there are four distinct weight distributions for the cosets of B . So our main result is about the even case. In a recent paper, Camion, Courteau, and Montpetit observe that for the lengths 15, 63, and 255 there are eight distinct weight tistributions. We prove that this property holds for the codes B and B for all even m.