On self-dual affine-invariant codes

Abstract : An extended cyclic code of length 2m over GF(2) cannot be self-dual for even m. For odd m, the Redd-Muller code [2m, 2m-1, 2(m+1)/2] is affine-invariant and self-dual and it is the only such code for m = 3 or 5. We describe the set of binary self-dual affine-invariant codes of length 2m for m = 7 and m = 9. For each m 3 9, we exhibit a self-dual affine-invariant code of length 2m over GF(2) which is not the self-dual Reed-Muller code. In the first part of the paper, we present the class of self-dual affine invariant codes of length 2rm over GF(2r) and the tools we apply later to the binary codes.
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Rapport
[Research Report] RR-1844, INRIA. 1993
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https://hal.inria.fr/inria-00074828
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Soumis le : mercredi 24 mai 2006 - 16:30:51
Dernière modification le : vendredi 25 mai 2018 - 12:02:03
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  • HAL Id : inria-00074828, version 1

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Pascale Charpin, Françoise Levy-Dit-Vehel. On self-dual affine-invariant codes. [Research Report] RR-1844, INRIA. 1993. 〈inria-00074828〉

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