Minimum Distance Decoding of General Algebraic Geometry Codes via Lists

摘要

Algebraic geometry codes are defined by divisors $D$ and $G$ on a curve over a finite field $BBF $. Often, $G$ is supported by a single $BBF $-rational point and the resulting code is called a one-point code. Recently, there has been interest in allowing the divisor $G$ to be more general as this can result in superior codes. In particular, one may obtain a code with better parameters by allowing $G$ to be supported by $m$ distinct $BBF $-rational points, where $m>1$. In this paper, we demonstrate that a multipoint algebraic geometry code $C$ may be embedded in a one-point code $C^{prime}$. Exploiting this fact, we obtain a minimum distance decoding algorithm for the multipoi-n-nnt code $C$. This is accomplished via list decoding in the one-point code $C^{prime}$.