Bounds on the minimum distance of the duals of BCH codes

Daniel Augot (1) , Françoise Levy-Dit-Vehel (1)

1 CODES - Coding and cryptography

We consider duals of BCH codes of length p^m-1 over GF(p). A lower bound on their minimum distance is found via the adaptation of the Weil bound to cyclic codes. However, this bound is of no significance for roughly half of these codes. We partially fill this gap by giving a lower bound for an infinite class of duals of BCH codes. We also present a lower bound obtained with an algorithm due to Massey and Schaub (1988). In the case of binary codes of length 127 and 255, the results are surprisingly higher than all previously known bounds

Domaines: Théorie de l'information [cs.IT]; Théorie de l'information et codage [math.IT]

Daniel Augot, Françoise Levy-Dit-Vehel. Bounds on the minimum distance of the duals of BCH codes. 1994 IEEE International Symposium on Information Theory, Jun 1994, Trondheim, Norway. pp.43, ⟨10.1109/ISIT.1994.394928⟩. ⟨inria-00509482⟩