The Nordstrom–Robinson Code is Algebraic-Geometric

Authors

Judy L. Walker, University of Nebraska - LincolnFollow

Document Type

Article

Date of this Version

1997

Citation

Published in IEEE Transactions on Information Theory, vol 43, iss 5 (Sept 1997), pp 1588-1593.

DOI: 10.1109/18.623154

Abstract

The techniques of algebraic geometry have been widely and successfully applied to the study of linear codes over finite field since the early 1980’s. Recently, there has been an increased interest in the study of linear codes over finite rings. In a previous paper [10], we combined these two approaches to coding theory by introducing and studying algebraic-geometric codes over rings. In this correspondence, we show that the Nordstrom–Robinson code is the image under the Gray mapping of an algebraic geometric code over Z = 4Z.