<p>Let <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12190_2025_2433_Article_IEq3.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="18" /> </InlineMediaObject> <EquationSource Format="TEX">$\mathbb F_q$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="double-struck">F</mi> <mi>q</mi> </msub> </math></EquationSource> </InlineEquation> denote the finite field of order <i>q</i>. In this paper, we investigate the permutation property of some new classes of permutation trinomials and pentanomials over <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12190_2025_2433_Article_IEq4.gif" Format="GIF" Height="18" Rendition="HTML" Resolution="72" Type="Linedraw" Width="37" /> </InlineMediaObject> <EquationSource Format="TEX">$\mathbb F_{3^{2m}}.$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi mathvariant="double-struck">F</mi> <msup> <mn>3</mn> <mrow> <mn>2</mn> <mi>m</mi> </mrow> </msup> </msub> <mo>.</mo> </mrow> </math></EquationSource> </InlineEquation> More precisely, based on some lower degree trinomials, we construct two new classes of permutation trinomials. Further, we prove the permutation property of five new classes of permutation pentanomials using both reducible and irreducible pentanomials of degree four and six over <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12190_2025_2433_Article_IEq5.gif" Format="GIF" Height="18" Rendition="HTML" Resolution="72" Type="Linedraw" Width="32" /> </InlineMediaObject> <EquationSource Format="TEX">$\mathbb F_{3^{2m}}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="double-struck">F</mi> <msup> <mn>3</mn> <mrow> <mn>2</mn> <mi>m</mi> </mrow> </msup> </msub> </math></EquationSource> </InlineEquation>.</p>

On some new classes of permutation trinomials and pentanomials over $ \mathbb F_{3^{2m}}$

期刊论文
发表日期：

2025年3月10日

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Shalini Gupta,
Sagar Vinayak,
Anand Nayyar,
Manpreet Singh

摘要

Let $\mathbb F_q$ $F_{q}$ denote the finite field of order q. In this paper, we investigate the permutation property of some new classes of permutation trinomials and pentanomials over $\mathbb F_{3^{2m}}.$ $F_{3^{2 m}} .$ More precisely, based on some lower degree trinomials, we construct two new classes of permutation trinomials. Further, we prove the permutation property of five new classes of permutation pentanomials using both reducible and irreducible pentanomials of degree four and six over $\mathbb F_{3^{2m}}$ $F_{3^{2 m}}$ .

On some new classes of permutation trinomials and pentanomials over \( \mathbb F_{3^{2m}}\)

摘要