We study perfect errorcorrectingcodes in which the codewords are protected by Hamming spheres of distinct protective radii. These codes have been introduced by Cohen, Montaron and Frankl [3, 4, 10]. We are intereste...
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Most of the applications of the DFT in the field of error control coding do not make use of the full power of the transform because the signal domain does not coincide with but is a subfield of the spectral domain. In...
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Cyclic codes which are invariant under the affine group are here described in a group algebra. A minimum system of generators for the extended codes is obtained from the zeros set of the cyclic code. We characterize t...
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We give a constructive characterization of all self dual 2n circulant codes over F2r. This construction generalizes those of F. J. MacWilliams [3], and G.F.M. Beenker [1]. Our method is original. We also give the numb...
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We introduce and characterize s-sum-sets which are a natural extension of partial-difference-sets and triple-sum-sets. We show that if Ω is the set of coordinate forms of C(n,k) and if X=F*Ω is an s-sum-set then C(n...
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This paper describes the algorithms used in an implementation of rational function integration in SAC-2, and gives a complexity analysis. The routines compute the transcendental part of the integral, expressing it ove...
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We have done some numerical experiments to find large coset leaders for the first order Reed-Muller codes RM(m) of length 2m for odd m,m ≥ 9, by using some matrix groups acting on the field GF(2m) viewed as a GF(2)-v...
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