Three Weight Ternary Linear Codes from Non-Weakly Regular Bent Functions

Rumi Melih Pelen

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arXiv · 2201.07113

Three Weight Ternary Linear Codes from Non-Weakly Regular Bent Functions

Rumi Melih Pelen

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Abstract

In this paper, several classes of three-weight ternary linear codes from non-weakly regular dual-bent functions are constructed based on a generic construction method. Instead of the whole space, we use the subspaces $B_+(f)$ or $B_-(f)$ associated with a ternary non-weakly regular dual-bent function $f$. Unusually, we use the pre-image sets of the dual function $f^*$ in $B_+(f)$ or $B_-(f)$ as the defining sets of the corresponding codes. Since the size of the defining sets of the constructed codes is flexible, it enables us to construct several codes with different parameters for a fixed dimension. We represent the weight distribution of the constructed codes. We also give several examples.

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Rumi Melih Pelen. 2022-01-18. Three Weight Ternary Linear Codes from Non-Weakly Regular Bent Functions. https://arxiv.org/abs/2201.07113

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