A generalization of algebraic-geometry codes

Chaoping Xing, Harald Niederreiter, Kwok-Yan Lam

Abstract: A generalization of algebraic-geometry codes based on function fields over finite fields with many places of small degree is presented. It turns out that many good linear codes can be obtained from these generalized algebraic-geometry codes. In particular, we calculate some examples of q-ary linear codes for q=2,3, 5. These examples show that many best possible linear codes can be found from our construction.