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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Weights in codes and genus 2 curves


Authors: Gary McGuire and José Felipe Voloch
Journal: Proc. Amer. Math. Soc. 133 (2005), 2429-2437
MSC (2000): Primary 94B15, 11G20
Published electronically: March 15, 2005
MathSciNet review: 2138886
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Abstract: We discuss a class of binary cyclic codes and their dual codes. The minimum distance is determined using algebraic geometry and an application of Weil's theorem. We relate each weight appearing in the dual codes to the number of rational points on a genus 2 curve of 2-rank 1 over a finite field of characteristic 2. The possible values for the number of points on a curve of genus 2 and 2-rank 1 are determined, thus determining the weights in the dual codes.


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Additional Information

Gary McGuire
Affiliation: Department of Mathematics, National University of Ireland, Maynooth, Co. Kildare, Ireland

José Felipe Voloch
Affiliation: Department of Mathematics, University of Texas, Austin, Texas 78712

DOI: http://dx.doi.org/10.1090/S0002-9939-05-08027-5
PII: S 0002-9939(05)08027-5
Received by editor(s): May 19, 2003
Received by editor(s) in revised form: February 6, 2004
Published electronically: March 15, 2005
Communicated by: Wen-Ching Winnie Li
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.