Goppa codes and trace operator

Abstract

We study Goppa codes, /spl Gamma/(L,g), defined by the polynomial g(z)=a(z)TrF/sub p/ms:F/sub p/s(b(z)). It is shown that the dimension of these codes never reaches the general, well-known, bound for Goppa codes. New bounds are proposed depending on the value of m and p. Furthermore, we prove that when p=2 these codes have only even weights.