تقرير
Construction of Permutation Polynomials over Finite Fields with the help of SCR polynomials
| العنوان: | Construction of Permutation Polynomials over Finite Fields with the help of SCR polynomials |
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| المؤلفون: | Sharma, Bidushi, Basnet, Dhiren Kumar |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Number Theory, 11T06, 11T55 |
| الوصف: | In this paper we take a deeper look at the self conjugate reciprocal (SCR) polynomials, which towards the end of the paper aid the construction of new classes of permutation trinomials and quadrinomials over $\mathbb{F}_{q^{2}}$. The paper focuses on the conditions required for a certain class of degree 2 and degree 3 SCR polynomials to have no roots in $\mu_{q+1}$ (the set of $(q+1)-\emph{th}$ roots of unity), which helps in the determination of polynomials that permute $\mathbb{F}_{q^{2}}$. In the due course we also look upon some higher degree SCR polynomials which can be reduced down to a degree 2 SCR polynomial over both odd and even ordered fields. We furthur look upon the SCR polynomials of type $ax^{q+1}+bx^{q}+bx+a^{q}$ taking both the cases under consideration where $a\in \mathbb{F}_{q}$ and $a\in\mathbb{F}_{q^{2}}\setminus\mathbb{F}_{q}$. Comment: 17 pages |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2404.00927 |
| رقم الأكسشن: | edsarx.2404.00927 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |