The Nordstrom-Robinson code is algebraic-geometric

Abstract

The techniques of algebraic geometry have been widely and successfully applied to the study of linear codes over finite fields since the early 1980s. There has also been an increased interest in the study of linear codes over finite rings. In a previous paper, we combined these two approaches to coding theory by introducing and studying algebraic-geometric codes over rings. We show that the Nordstrom-Robinson code is the image under the Gray mapping of an algebraic-geometric code over Z/4Z.