On self-dual affine-invariant codes

Pascale Charpin (1) , Françoise Levy-Dit-Vehel (1)

1 CODES - Coding and cryptography

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.

Domaines: Autre [cs.OH]

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