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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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Contributor : Rapport de Recherche Inria Connect in order to contact the contributor
Submitted on : Wednesday, May 24, 2006 - 4:30:51 PM
Last modification on : Thursday, April 14, 2022 - 1:58:01 PM
Long-term archiving on: : Tuesday, April 12, 2011 - 4:05:38 PM


  • HAL Id : inria-00074828, version 1



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



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