Minimum Distance Decoding of General Algebraic Geometry Codes via Lists

Algebraic geometry codes are defined by divisors
D
and
G
on a curve over a finite field F. Often,
G
is supported by a single F-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 F-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'
. Exploiting this fact, we obtain a minimum distance decoding algorithm for the multipoint code
C
. This is accomplished via list decoding in the one-point code C'.