Weights in codes and genus 2 curves

McGuire, Gary; Voloch, José

doi:10.1090/S0002-9939-05-08027-5

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
DOI: https://doi.org/10.1090/S0002-9939-05-08027-5
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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