Date of this Version
Published in Codes, Curves, and Signals: Common Threads in Communications (A. Vardy, ed.), The Springer International Series in Engineering and Computer Science (Communications and Information Theory), vol 485. Boston: Kluwer Academic Publishers. (1998) pp. 53-62.
In [15: J. L. Walker, Algebraic geometric codes over rings], the second author defined algebraic geometric codes over rings. This definition was motivated by two recent trends in coding theory: the study of algebraic geometric codes over finite fields, and the study of codes over rings. In that paper, many of the basic parameters of these new codes were computed. However, the Lee weight, which is very important for codes over the ring Z/4Z, was not considered. In [14: J.-F. Voloch and J. L. Walker, Euclidean weights of codes from elliptic curves over rings], this weight measure, as well as the more general Euclidean weight for codes over Z/plZ, is considered for algebraic geometric codes arising from elliptic curves. In this paper, we will focus on the specific case of codes over Z/4Z and we will show how everything works in an explicit example.