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
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by Gary McGuire and José Felipe Voloch PDF

Proc. Amer. Math. Soc. 133 (2005), 2429-2437 Request permission

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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