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Finding the defining functions for one-point algebraic-geometry codes

Authors :
Douglas A. Leonard
Source :
IEEE Transactions on Information Theory. 47:2566-2573
Publication Year :
2001
Publisher :
Institute of Electrical and Electronics Engineers (IEEE), 2001.

Abstract

An iterative algorithm is given for producing the parity-check functions for one-point algebraic-geometry (AG) codes, in particular (but not limited to) those related to the two towers of function fields introduced by Garcia and Stichtenoth (1995). This simple method, based on the linearity of the Qth-power map over F/sub Q/, is an alternative to the method of using Laurent series expansions. Examples are given for small values of m with characteristic p=2 for both towers.

Subjects

Subjects :
Discrete mathematics
Function field of an algebraic variety
Laurent series
Algebraic surface
Real algebraic geometry
Algebraic function
Library and Information Sciences
Differential algebraic geometry
Addition theorem
Algebraic geometry and analytic geometry
Computer Science Applications
Information Systems
Mathematics

Details

ISSN :
00189448
Volume :
47
Database :
OpenAIRE
Journal :
IEEE Transactions on Information Theory
Accession number :
edsair.doi...........801cb3b31a84c934d23b0f2ac8009d93
Full Text :
https://doi.org/10.1109/18.945271
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