An improved Serre bound for elementary abelian extensions ofF_q(x) and the generalized Hamming weights of duals of BCHcodes

摘要

An improvement on the Serre bound for the number of rationalplaces is obtained here. Using our result we improve the bounds on thegeneralized Hamming weights of the duals of the BCH codes estimated byStichtenoth and Voss (see IEEE Trans. Inform. Theory, vol.40, no.2,p.554-8, 1994). Our new bound is tight in the binary case of thegeneralized Hamming weight of BCH(2)⊥