Finite Fields and Their Applications最新文献_第8页

Saturating linear sets in PG(2,q4) PG(2,q4) 中的饱和线性集合

IF 1 3区数学

Finite Fields and Their Applications Pub Date : 2024-05-21 DOI: 10.1016/j.ffa.2024.102447

Ferdinando Zullo

引用次数: 0

On the generalized Fibonacci sequences of polynomials over finite fields 论有限域上多项式的广义斐波那契序列

IF 1 3区数学

Finite Fields and Their Applications Pub Date : 2024-05-15 DOI: 10.1016/j.ffa.2024.102446

Zekai Chen, Min Sha, Chen Wei

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On the Rosenhain forms of superspecial curves of genus two 论二属超特殊曲线的罗森海恩形式

IF 1 3区数学

Finite Fields and Their Applications Pub Date : 2024-05-13 DOI: 10.1016/j.ffa.2024.102445

Ryo Ohashi

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Nilpotent linearized polynomials over finite fields, revisited 有限域上的无势线性化多项式，再论

IF 1 3区数学

Finite Fields and Their Applications Pub Date : 2024-05-08 DOI: 10.1016/j.ffa.2024.102442

Daniel Panario , Lucas Reis

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Finite period vectors and Gauss sums 有限周期向量和高斯和

IF 1 3区数学

Finite Fields and Their Applications Pub Date : 2024-05-06 DOI: 10.1016/j.ffa.2024.102443

Yeongseong Jo

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Binary and ternary leading-systematic LCD codes from special functions 来自特殊函数的二进制和三元前导系统 LCD 代码

IF 1 3区数学

Finite Fields and Their Applications Pub Date : 2024-05-03 DOI: 10.1016/j.ffa.2024.102441

Xiaoru Li , Ziling Heng

{"title":"Binary and ternary leading-systematic LCD codes from special functions","authors":"Xiaoru Li , Ziling Heng","doi":"10.1016/j.ffa.2024.102441","DOIUrl":"https://doi.org/10.1016/j.ffa.2024.102441","url":null,"abstract":"<div>Linear complementary dual codes (LCD codes for short) are an important subclass of linear codes which have nice applications in communication systems, cryptography, consumer electronics and information protection. In the literature, it has been proved that an <math><mo>[</mo><mi>n</mi><mo>,</mo><mi>k</mi><mo>,</mo><mi>d</mi><mo>]</mo></math> Euclidean LCD code over <math><msub><mrow><mi>F</mi></mrow><mrow><mi>q</mi></mrow></msub></math> with <math><mi>q</mi><mo>></mo><mn>3</mn></math> exists if there is an <math><mo>[</mo><mi>n</mi><mo>,</mo><mi>k</mi><mo>,</mo><mi>d</mi><mo>]</mo></math> linear code over <math><msub><mrow><mi>F</mi></mrow><mrow><mi>q</mi></mrow></msub></math>, where q is a prime power. However, the existence of binary and ternary Euclidean LCD codes has not been totally characterized. Hence it is interesting to construct binary and ternary Euclidean LCD codes with new parameters. In this paper, we construct new families of binary and ternary leading-systematic Euclidean LCD codes from some special functions including semibent functions, quadratic functions, almost bent functions, and planar functions. These LCD codes are not constructed directly from such functions, but come from some self-orthogonal codes constructed with such functions. Compared with known binary and ternary LCD codes, the LCD codes in this paper have new parameters.</div>","PeriodicalId":50446,"journal":{"name":"Finite Fields and Their Applications","volume":"97 ","pages":"Article 102441"},"PeriodicalIF":1.0,"publicationDate":"2024-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140824498","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

On the number of k-normal elements and Fq-practical numbers 关于 k 法向元素数和 Fq 实用数

IF 1 3区数学

Finite Fields and Their Applications Pub Date : 2024-05-02 DOI: 10.1016/j.ffa.2024.102444

Josimar J.R. Aguirre, Victor G.L. Neumann

引用次数: 0

Binary sequence family with both small cross-correlation and large family complexity 交叉相关性小而族复杂性大的二进制序列族

IF 1 3区数学

Finite Fields and Their Applications Pub Date : 2024-04-29 DOI: 10.1016/j.ffa.2024.102440

Huaning Liu, Xi Liu

引用次数: 0

Iterative constructions of irreducible polynomials from isogenies 从等差数列迭代构造不可约多项式

IF 1 3区数学

Finite Fields and Their Applications Pub Date : 2024-04-17 DOI: 10.1016/j.ffa.2024.102429

Alp Bassa , Gaetan Bisson , Roger Oyono

{"title":"Iterative constructions of irreducible polynomials from isogenies","authors":"Alp Bassa , Gaetan Bisson , Roger Oyono","doi":"10.1016/j.ffa.2024.102429","DOIUrl":"https://doi.org/10.1016/j.ffa.2024.102429","url":null,"abstract":"<div>Let S be a rational fraction and let f be a polynomial over a finite field. Consider the transform <math><mi>T</mi><mo>(</mo><mi>f</mi><mo>)</mo><mo>=</mo><mi>numerator</mi><mo>(</mo><mi>f</mi><mo>(</mo><mi>S</mi><mo>)</mo><mo>)</mo></math>. In certain cases, the polynomials f, <math><mi>T</mi><mo>(</mo><mi>f</mi><mo>)</mo></math>, <math><mi>T</mi><mo>(</mo><mi>T</mi><mo>(</mo><mi>f</mi><mo>)</mo><mo>)</mo><mo>…</mo></math> are all irreducible. For instance, in odd characteristic, this is the case for the rational fraction <math><mi>S</mi><mo>=</mo><mo>(</mo><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>+</mo><mn>1</mn><mo>)</mo><mo>/</mo><mo>(</mo><mn>2</mn><mi>x</mi><mo>)</mo></math>, known as the R-transform, and for a positive density of irreducible polynomials f. We interpret these transforms in terms of isogenies of elliptic curves. Using complex multiplication theory, we devise algorithms to generate a large number of rational fractions S, each of which yields infinite families of irreducible polynomials for a positive density of starting irreducible polynomials f.</div>","PeriodicalId":50446,"journal":{"name":"Finite Fields and Their Applications","volume":"97 ","pages":"Article 102429"},"PeriodicalIF":1.0,"publicationDate":"2024-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S1071579724000686/pdfft?md5=a6523cce78fcf25021f82a37e1682042&pid=1-s2.0-S1071579724000686-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140559242","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

The p-rank of curves of Fermat type 费马型曲线的 p 级

IF 1 3区数学

Finite Fields and Their Applications Pub Date : 2024-04-16 DOI: 10.1016/j.ffa.2024.102430

Herivelto Borges , Cirilo Gonçalves

{"title":"The p-rank of curves of Fermat type","authors":"Herivelto Borges , Cirilo Gonçalves","doi":"10.1016/j.ffa.2024.102430","DOIUrl":"https://doi.org/10.1016/j.ffa.2024.102430","url":null,"abstract":"<div>Let <math><mi>K</mi></math> be an algebraically closed field of characteristic <math><mi>p</mi><mo>></mo><mn>0</mn></math>. A pressing problem in the theory of algebraic curves is the determination of the p-rank of a (nonsingular, projective, irreducible) curve <math><mi>X</mi></math> over <math><mi>K</mi></math>. This birational invariant affects arithmetic and geometric properties of <math><mi>X</mi></math>, and its fundamental role in the study of the automorphism group <math><mi>Aut</mi><mo>(</mo><mi>X</mi><mo>)</mo></math> has been noted by many authors in the past few decades. In this paper, we provide an extensive study of the p-rank of curves of Fermat type <math><msup><mrow><mi>y</mi></mrow><mrow><mi>m</mi></mrow></msup><mo>=</mo><msup><mrow><mi>x</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>+</mo><mn>1</mn></math> over <math><mi>K</mi><mo>=</mo><msub><mrow><mover><mrow><mi>F</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mi>p</mi></mrow></msub></math>. We determine a combinatorial formula for this invariant in the general case and show how this leads to explicit formulas of the p-rank of several such curves. By way of illustration, we present explicit formulas for more than twenty subfamilies of such curves, where m and n are generally given in terms of p. We also show how the approach can be used to compute the p-rank of other types of curves.</div>","PeriodicalId":50446,"journal":{"name":"Finite Fields and Their Applications","volume":"97 ","pages":"Article 102430"},"PeriodicalIF":1.0,"publicationDate":"2024-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140555141","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0