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arXiv · 1212.6371

The Weight Distribution of a Class of Cyclic Codes Related to Hermitian Forms Graphs

Shuxing Li·Sihuang Hu·Tao Feng·Gennian Ge
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Abstract

The determination of weight distribution of cyclic codes involves evaluation of Gauss sums and exponential sums. Despite of some cases where a neat expression is available, the computation is generally rather complicated. In this note, we determine the weight distribution of a class of reducible cyclic codes whose dual codes may have arbitrarily many zeros. This goal is achieved by building an unexpected connection between the corresponding exponential sums and the spectrums of Hermitian forms graphs.

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Shuxing Li, Sihuang Hu, Tao Feng, Gennian Ge. 2012-12-27. The Weight Distribution of a Class of Cyclic Codes Related to Hermitian Forms Graphs. https://doi.org/10.1109/tit.2013.2242957

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