On even codes (Q1185087)

Even self-orthogonal codes over \(GF(2^ m)\) are introduced. If \(GF(2^ m)\) is identified with \((GF(2))^ m\) using a self-complementary basis, such codes become binary codes in which all weights are multiples of four. Extended Reed-Solomon codes of rate \(\leq 1/2\) turn out to be even. Asymptotically good even self-dual codes arise (as geometric Goppa codes) from the class field tower method used by Serre to obtain curves with many rational points.