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/sup /spl perp// of the binary cyclic codes C of length n=2/sup m/-1 with zeros /spl alpha/, /spl alpha//sup 2(t-1+1)/, /spl alpha/(2/sup t/+1). Here m=2t+1 and /spl alpha/ generate the multiplicative group of the finite field F/sub 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/sup /spl perp//. Indeed, combining theorem 15 (ii)-1 in Kasami with the fact that the minimum distance d/sub min/=7 (see MacWilliams and Sloane, 1983) also yields the weight distribution of C/sup /spl perp//.