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

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1 Author(s)
van der Vlugt, M. ; Math. Inst., Leiden Univ., Netherlands

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=2m-1 with zeros α, α2(t-1+1), α(2t+1). Here m=2t+1 and α generate the multiplicative group of the finite field F2m. 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 dmin=7 (see MacWilliams and Sloane, 1983) also yields the weight distribution of C

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Information Theory, IEEE Transactions on  (Volume:43 ,  Issue: 5 )