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

摘要

Let B be the binary two-error-correcting BCH code of length 2/sup m/-1 and let B/spl circ/ be the extended code of B. We give formal expressions of weight distributions of the cosets of the codes B/spl circ/ 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. Camion, Courteau, and Montpetit (see ibid., vol.38, no.7, p.1353, 1992) observe that for the lengths 15, 63, and 255 there are eight distinct weight distributions. We prove that this property holds for the codes B/spl circ/ and B for all even m.