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Mathematics 2016, 4(2), 32; doi:10.3390/math4020032

On the Dimension of Algebraic-Geometric Trace Codes

1
Department of Mathematics and Computer Science, Goucher College, Baltimore, MD 21204, USA
2
Department of Mathematics, College of Saint Benedict and Saint John’s University, Collegeville, MN 56321, USA
*
Author to whom correspondence should be addressed.
Academic Editor: Hari M. Srivastava
Received: 29 January 2016 / Revised: 21 April 2016 / Accepted: 22 April 2016 / Published: 7 May 2016
View Full-Text   |   Download PDF [234 KB, uploaded 7 May 2016]

Abstract

We study trace codes induced from codes defined by an algebraic curve X. We determine conditions on X which admit a formula for the dimension of such a trace code. Central to our work are several dimension reducing methods for the underlying functions spaces associated to X. View Full-Text
Keywords: error correcting codes; trace codes; exponential sums; number theory; 11T71 error correcting codes; trace codes; exponential sums; number theory; 11T71
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Le, P.; Chetty, S. On the Dimension of Algebraic-Geometric Trace Codes. Mathematics 2016, 4, 32.

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