Minimum Distance of Goppa Codes

  title={Minimum Distance of Goppa Codes},
  author={Arnaldo Garcia and Seon Jeong Kim and Robert F. Lax},
We prove that if there are consecutive gaps at a rational point on a smooth curve defined over a finite field, then one can improve the usual lower bound on the minimum distance of certain algebraic-geometric codes defined using a multiple of the point. A q-ary linear code of length n and dimension k is a vector subspace of dimension k of Fq , where Fq denotes the finite field with q elements. The minimum distance of a code is the minimum number of places in which two distinct codewords differ… CONTINUE READING