Minimum distance decoding of general algebraic geometry codes via lists

Authors:
Nathan Drake;Gretchen L. Matthews
Affiliations:
Department of Mathematics, North Greenville University, Tigerville, SC;Department of Mathematical Sciences, Clemson University, Clemson, SC
Venue:
IEEE Transactions on Information Theory
Year:
2010

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Abstract

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′.