Algebraic geometric codes over rings

The techniques of algebraic geometry have been widely and successfully appl ied to the study of linear codes over finite fields since the early 1980s. Recently, there has been an increased interest in the study of linear codes over finite rings. In this paper, we combine these two approaches to codin g theory by introducing the study of algebraic geometric codes over rings. In addition to defining these new codes, we prove several results about the ir properties. (C) 1999 Elsevier Science B.V. All rights reserved.