The Weight Hierarchy of Some Reducible Cyclic Codes

Maosheng Xiong; Shuxing Li; Gennian Ge

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arXiv · 1504.01274

The Weight Hierarchy of Some Reducible Cyclic Codes

Maosheng Xiong·Shuxing Li·Gennian Ge

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Abstract

The generalized Hamming weights (GHWs) of linear codes are fundamental parameters, the knowledge of which is of great interest in many applications. However, to determine the GHWs of linear codes is difficult in general. In this paper, we study the GHWs for a family of reducible cyclic codes and obtain the complete weight hierarchy in several cases. This is achieved by extending the idea of \cite{YLFL} into higher dimension and by employing some interesting combinatorial arguments. It shall be noted that these cyclic codes may have arbitrary number of nonzeroes.

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Maosheng Xiong, Shuxing Li, Gennian Ge. 2015-04-06. The Weight Hierarchy of Some Reducible Cyclic Codes. https://arxiv.org/abs/1504.01274

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