Finite Fields and Their Applications最新文献_第3页

Explicit representatives and sizes of cyclotomic cosets and their application to cyclic codes over finite fields 有限域上环切集的显式表示和大小及其在循环码中的应用

IF 1.2 3区数学

Finite Fields and Their Applications Pub Date : 2026-03-01 Epub Date: 2025-11-25 DOI: 10.1016/j.ffa.2025.102761

Li Zhu , Jinle Liu , Hongfeng Wu

{"title":"Explicit representatives and sizes of cyclotomic cosets and their application to cyclic codes over finite fields","authors":"Li Zhu , Jinle Liu , Hongfeng Wu","doi":"10.1016/j.ffa.2025.102761","DOIUrl":"10.1016/j.ffa.2025.102761","url":null,"abstract":"<div><div>Cyclotomic coset is a classical notion in the theory of finite fields which has wide applications in various computation problems. Let q be a prime power, and n be a positive integer coprime to q. In this paper we determine explicitly the representatives and the sizes of all q-cyclotomic cosets modulo n in the general settings. We introduce the definition of 2-adic cyclotomic system, which is a profinite space consists of certain compatible sequences of cyclotomic cosets. A precise characterization of the structure of the 2-adic cyclotomic system is given, which reveals the general formula for representatives of cyclotomic cosets. With the representatives and the sizes of q-cyclotomic cosets modulo n, we improve the formulas for the factorizations of <math><msup><mrow><mi>X</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>−</mo><mn>1</mn></math> and of <math><msub><mrow><mi>Φ</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>(</mo><mi>X</mi><mo>)</mo></math> over <math><msub><mrow><mi>F</mi></mrow><mrow><mi>q</mi></mrow></msub></math> given in [4]. As a consequence, we classify the cyclic codes over finite fields via giving their generator polynomials. Moreover, the self-dual cyclic codes are determined and enumerated.</div></div>","PeriodicalId":50446,"journal":{"name":"Finite Fields and Their Applications","volume":"111 ","pages":"Article 102761"},"PeriodicalIF":1.2,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145624202","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

New curves of Kummer type with many rational points over finite fields 有限域上具有多有理点的Kummer型新曲线

IF 1.2 3区数学

Finite Fields and Their Applications Pub Date : 2026-03-01 Epub Date: 2025-12-16 DOI: 10.1016/j.ffa.2025.102780

H. Navarro, Luz A. Pérez

引用次数: 0

One class of maximal cliques in the collinearity graphs of geometries related to simplex codes 与单纯形码相关的几何共线性图中的一类极大团

IF 1.2 3区数学

Finite Fields and Their Applications Pub Date : 2026-03-01 Epub Date: 2025-12-15 DOI: 10.1016/j.ffa.2025.102784

Mariusz Kwiatkowski, Mark Pankov, Adam Tyc

引用次数: 0

Criteria of maximality and minimality of van der Geer–van der Vlugt curves van der Geer-van der Vlugt曲线的极大极小准则

IF 1.2 3区数学

Finite Fields and Their Applications Pub Date : 2026-03-01 Epub Date: 2025-12-11 DOI: 10.1016/j.ffa.2025.102781

Tetsushi Ito , Ren Tatematsu , Takahiro Tsushima

引用次数: 0

On the Hermitian Veronesean 在厄米特的维罗内西亚

IF 1.2 3区数学

Finite Fields and Their Applications Pub Date : 2026-03-01 Epub Date: 2025-11-21 DOI: 10.1016/j.ffa.2025.102762

John Bamberg , Geertrui Van de Voorde

引用次数: 0

On the PGL2(q)-orbits of lines of PG(3,q) and binary quartic forms in characteristic three 特征三中PG（3,q）和二元四次型线的PGL2(q)轨道

IF 1.2 3区数学

Finite Fields and Their Applications Pub Date : 2026-03-01 Epub Date: 2025-11-26 DOI: 10.1016/j.ffa.2025.102763

Krishna Kaipa , Puspendu Pradhan

引用次数: 0

A new family of maximum linear symmetric rank-distance codes 一类新的最大线性对称秩距码

IF 1.2 3区数学

Finite Fields and Their Applications Pub Date : 2026-03-01 Epub Date: 2026-01-02 DOI: 10.1016/j.ffa.2025.102787

Wei Tang , Yue Zhou

引用次数: 0

On the addition of squares and cubes of units modulo n 关于以n为模的单位的平方和立方的加法

IF 1.2 3区数学

Finite Fields and Their Applications Pub Date : 2026-03-01 Epub Date: 2025-12-15 DOI: 10.1016/j.ffa.2025.102778

Yajing Zhou , Rongquan Feng

引用次数: 0

A provably quasi-polynomial algorithm for the discrete logarithm problem in finite fields of small characteristic 小特征有限域中离散对数问题的可证明拟多项式算法

IF 1.2 3区数学

Finite Fields and Their Applications Pub Date : 2026-03-01 Epub Date: 2025-11-20 DOI: 10.1016/j.ffa.2025.102753

Guido Lido

引用次数: 0

Infinite families of non-simple subspace 2- and 3-designs with block dimension 4 块维为4的非简单子空间2-和3-设计的无限族

IF 1.2 3区数学

Finite Fields and Their Applications Pub Date : 2026-03-01 Epub Date: 2025-12-30 DOI: 10.1016/j.ffa.2025.102786

Xiaoran Wang, Junling Zhou

{"title":"Infinite families of non-simple subspace 2- and 3-designs with block dimension 4","authors":"Xiaoran Wang, Junling Zhou","doi":"10.1016/j.ffa.2025.102786","DOIUrl":"10.1016/j.ffa.2025.102786","url":null,"abstract":"<div><div>This paper concentrates on constructing infinite families of non-simple subspace 2-designs and 3-designs with block dimension 4. We investigate in detail the structure of the <math><mrow><mi>GL</mi></mrow><mo>(</mo><mi>m</mi><mo>,</mo><msup><mrow><mi>q</mi></mrow><mrow><mi>l</mi></mrow></msup><mo>)</mo></math>-incidence matrix between 2-subspaces and 4-subspaces of <math><mi>GF</mi><mspace></mspace><msup><mrow><mo>(</mo><mi>q</mi><mo>)</mo></mrow><mrow><mi>m</mi><mi>l</mi></mrow></msup></math> with <math><mi>m</mi><mo>,</mo><mi>l</mi><mo>≥</mo><mn>3</mn></math>. Employing the incidence matrix, we establish two recursive constructions for 2-<math><msub><mrow><mo>(</mo><mi>m</mi><mi>l</mi><mo>,</mo><mn>4</mn><mo>,</mo><mi>λ</mi><mo>)</mo></mrow><mrow><mi>q</mi></mrow></msub></math> designs, which are based on a 2-<math><msub><mrow><mo>(</mo><mi>l</mi><mo>,</mo><mn>4</mn><mo>,</mo><mi>λ</mi><mo>)</mo></mrow><mrow><mi>q</mi></mrow></msub></math> design and a 2-<math><msub><mrow><mo>(</mo><mi>l</mi><mo>,</mo><mn>3</mn><mo>,</mo><mi>μ</mi><mo>)</mo></mrow><mrow><mi>q</mi></mrow></msub></math> design, respectively. Several new infinite classes of simple q-analogs of group divisible designs (q-GDDs) with block dimension 4 are also produced. Making use of the recursive constructions and new q-GDDs, plenty of new infinite series of non-simple subspace 2-designs with block dimension 4 are constructed. We also study the <math><mi>GL</mi><mo>(</mo><mi>m</mi><mo>,</mo><msup><mrow><mi>q</mi></mrow><mrow><mi>l</mi></mrow></msup><mo>)</mo></math>-incidence matrix between 3-subspaces and 4-subspaces. From this, a recursive construction and a new infinite family of non-simple 3-<math><msub><mrow><mo>(</mo><mi>m</mi><mi>l</mi><mo>,</mo><mn>4</mn><mo>,</mo><mi>λ</mi><mo>)</mo></mrow><mrow><mi>q</mi></mrow></msub></math> designs are produced as well.</div></div>","PeriodicalId":50446,"journal":{"name":"Finite Fields and Their Applications","volume":"111 ","pages":"Article 102786"},"PeriodicalIF":1.2,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145883539","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