On even codes

AbstractThe notion of an even selforthogonal code is introduced over Fq, q = 2m, in such a way that codes with this property become ordinary even binary codes (i.e., all weights are multiples of 4) whenFq is identified with Fm2 using aselfcomplementary basis. Extended Reed-Solomon codes of rate ⩽12 turn out to be even. Furthermore, it is shown that asymptotically good even selfdual codes arise from the class field tower method used by Serre to obtain curves with many Fq-rational points