Families of curves and weight distributions of codes

Schoof, René

doi:10.1090/S0273-0979-1995-00586-0

Families of curves and weight distributions of codes
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Bull. Amer. Math. Soc. 32 (1995), 171-183 Request permission

Abstract:

In this expository paper we show how one can, in a uniform way, calculate the weight distributions of some well-known binary cyclic codes. The codes are related to certain families of curves, and the weight distributions are related to the distribution of the number of rational points on the curves.

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