Addendum to “Non-BCH triple-error-correcting codes”

For original paper see van der Vlugt (IEEE Trans. Inform. Theory, vol.42, p.1612-14, 1996). One of the subjects in the above-mentioned paper is the determination of the weight distribution of the dual code C ^⊥ of the binary cyclic codes C of length n=2^m-1 with zeros α, α^2(t-1+1), α(2^t+1). Here m=2t+1 and α generate the multiplicative group of the finite field F_2m. After the publication of van der Vlugt (1996), Tor Helleseth drew the present author´s attention to the fact that Kasami´s paper (1969) contains the key to an essentially different way of deriving the weight enumerator of C^⊥. Indeed, combining theorem 15 (ii)-1 in Kasami with the fact that the minimum distance d_min=7 (see MacWilliams and Sloane, 1983) also yields the weight distribution of C^⊥