On the Weight Distribution of Cyclic Codes with Niho Exponents

Shuxing Li; Tao Feng; Gennian Ge

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arXiv · 1401.1887

On the Weight Distribution of Cyclic Codes with Niho Exponents

Shuxing Li·Tao Feng·Gennian Ge

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Abstract

Recently, there has been intensive research on the weight distributions of cyclic codes. In this paper, we compute the weight distributions of three classes of cyclic codes with Niho exponents. More specifically, we obtain two classes of binary three-weight and four-weight cyclic codes and a class of nonbinary four-weight cyclic codes. The weight distributions follow from the determination of value distributions of certain exponential sums. Several examples are presented to show that some of our codes are optimal and some have the best known parameters.

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Shuxing Li, Tao Feng, Gennian Ge. 2014-01-09. On the Weight Distribution of Cyclic Codes with Niho Exponents. https://arxiv.org/abs/1401.1887

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