Differential uniformity and costacyclic code from some power mapping
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866912153383993344 |
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| author | Cui, Yuehui Luo, Jinquan |
| author_facet | Cui, Yuehui Luo, Jinquan |
| contents | In this paper, we study the differential properties of $x^d$ over $\mathbb{F}_{p^n}$ with $d=p^{2l}-p^{l}+1$. By studying the differential equation of $x^d$ and the number of rational points on some curves over finite fields, we completely determine differential spectrum of $x^{d}$. Then we investigate the $c$-differential uniformity of $x^{d}$. We also calculate the value distribution of a class of exponential sum related to $x^d$. In addition, we obtain a class of six-weight consta-cyclic codes, whose weight distribution is explicitly determined. Part of our results is a complement of the works shown in [\ref{H1}, \ref{H2}] which mainly focus on cross correlations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_08860 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Differential uniformity and costacyclic code from some power mapping Cui, Yuehui Luo, Jinquan Information Theory In this paper, we study the differential properties of $x^d$ over $\mathbb{F}_{p^n}$ with $d=p^{2l}-p^{l}+1$. By studying the differential equation of $x^d$ and the number of rational points on some curves over finite fields, we completely determine differential spectrum of $x^{d}$. Then we investigate the $c$-differential uniformity of $x^{d}$. We also calculate the value distribution of a class of exponential sum related to $x^d$. In addition, we obtain a class of six-weight consta-cyclic codes, whose weight distribution is explicitly determined. Part of our results is a complement of the works shown in [\ref{H1}, \ref{H2}] which mainly focus on cross correlations. |
| title | Differential uniformity and costacyclic code from some power mapping |
| topic | Information Theory |
| url | https://arxiv.org/abs/2412.08860 |