Finite Fields and Their Applications最新文献_第10页

The resultant method in higher dimensions 高维度结果法

IF 1.2 3区数学

Finite Fields and Their Applications Pub Date : 2024-08-30 DOI: 10.1016/j.ffa.2024.102493

N. Harrach , L. Storme , P. Sziklai , M. Takáts

引用次数: 0

A note on (2,2)-isogenies via theta coordinates 通过 Theta 坐标的 (2,2)-isogenies 注释

IF 1.2 3区数学

Finite Fields and Their Applications Pub Date : 2024-08-30 DOI: 10.1016/j.ffa.2024.102496

Jianming Lin , Saiyu Wang , Chang-An Zhao

{"title":"A note on (2,2)-isogenies via theta coordinates","authors":"Jianming Lin , Saiyu Wang , Chang-An Zhao","doi":"10.1016/j.ffa.2024.102496","DOIUrl":"10.1016/j.ffa.2024.102496","url":null,"abstract":"<div>In this paper, we revisit the algorithm for computing chains of <math><mo>(</mo><mn>2</mn><mo>,</mo><mn>2</mn><mo>)</mo></math>-isogenies between products of elliptic curves via theta coordinates proposed by Dartois et al. For each fundamental block of this algorithm, we provide an explicit inversion-free version. Besides, we exploit the technique of x-only ladder to speed up the computation of gluing isogeny. Finally, we present a mixed optimal strategy, which combines the inversion-elimination tool with the original methods together to execute a chain of <math><mo>(</mo><mn>2</mn><mo>,</mo><mn>2</mn><mo>)</mo></math>-isogenies.We make a cost analysis and present a concrete comparison between ours and the previously known methods for inversion elimination. Furthermore, we implement the mixed optimal strategy for benchmark. The results show that when computing <math><mo>(</mo><mn>2</mn><mo>,</mo><mn>2</mn><mo>)</mo></math>-isogeny chains with lengths of 126, 208 and 632, compared to Dartois, Maino, Pope and Robert's latest implementation, utilizing our techniques can reduce 9.7%, 9.5% and 9.6% multiplications over the base field <math><msub><mrow><mi>F</mi></mrow><mrow><mi>p</mi></mrow></msub></math>, respectively. Therefore, even for the updated version that employs their inversion-free algorithms, our tools still possess an advantage.</div>","PeriodicalId":50446,"journal":{"name":"Finite Fields and Their Applications","volume":"99 ","pages":"Article 102496"},"PeriodicalIF":1.2,"publicationDate":"2024-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142097567","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

Achromatic colorings of polarity graphs 极性图的消色性着色

IF 1.2 3区数学

Finite Fields and Their Applications Pub Date : 2024-08-30 DOI: 10.1016/j.ffa.2024.102497

Vladislav Taranchuk , Craig Timmons

引用次数: 0

On a recent extension of a family of biprojective APN functions 论双射 APN 函数族的最新扩展

IF 1.2 3区数学

Finite Fields and Their Applications Pub Date : 2024-08-27 DOI: 10.1016/j.ffa.2024.102494

Lukas Kölsch

引用次数: 0

Four new families of NMDS codes with dimension 4 and their applications 维数为 4 的 NMDS 代码的四个新系列及其应用

IF 1.2 3区数学

Finite Fields and Their Applications Pub Date : 2024-08-26 DOI: 10.1016/j.ffa.2024.102495

Yun Ding, Yang Li, Shixin Zhu

{"title":"Four new families of NMDS codes with dimension 4 and their applications","authors":"Yun Ding, Yang Li, Shixin Zhu","doi":"10.1016/j.ffa.2024.102495","DOIUrl":"10.1016/j.ffa.2024.102495","url":null,"abstract":"<div>For an <math><msub><mrow><mo>[</mo><mi>n</mi><mo>,</mo><mi>k</mi><mo>,</mo><mi>d</mi><mo>]</mo></mrow><mrow><mi>q</mi></mrow></msub></math> linear code <math><mi>C</mi></math>, the singleton defect of <math><mi>C</mi></math> is defined by <math><mi>S</mi><mo>(</mo><mi>C</mi><mo>)</mo><mo>=</mo><mi>n</mi><mo>−</mo><mi>k</mi><mo>+</mo><mn>1</mn><mo>−</mo><mi>d</mi></math>. When <math><mi>S</mi><mo>(</mo><mi>C</mi><mo>)</mo><mo>=</mo><mi>S</mi><mo>(</mo><msup><mrow><mi>C</mi></mrow><mrow><mo>⊥</mo></mrow></msup><mo>)</mo><mo>=</mo><mn>1</mn></math>, the code <math><mi>C</mi></math> is called a near maximum distance separable (NMDS) code, where <math><msup><mrow><mi>C</mi></mrow><mrow><mo>⊥</mo></mrow></msup></math> is the dual code of <math><mi>C</mi></math>. NMDS codes have important applications in finite projective geometries, designs and secret sharing schemes. In this paper, we present four new constructions of infinite families of NMDS codes with dimension 4 and completely determine their weight enumerators. As an application, we also determine the locality of the dual codes of these NMDS codes and obtain four families of distance-optimal and dimension-optimal locally recoverable codes.</div>","PeriodicalId":50446,"journal":{"name":"Finite Fields and Their Applications","volume":"99 ","pages":"Article 102495"},"PeriodicalIF":1.2,"publicationDate":"2024-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142075831","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 automorphism group of a family of maximal curves not covered by the Hermitian curve 论赫米曲线未覆盖的最大曲线族的自变群

IF 1.2 3区数学

Finite Fields and Their Applications Pub Date : 2024-08-26 DOI: 10.1016/j.ffa.2024.102498

Maria Montanucci , Guilherme Tizziotti , Giovanni Zini

引用次数: 0

The subspace structure of maximum cliques in pseudo-Paley graphs from unions of cyclotomic classes 从循环类的联合看伪帕利图中最大小群的子空间结构

IF 1.2 3区数学

Finite Fields and Their Applications Pub Date : 2024-08-14 DOI: 10.1016/j.ffa.2024.102492

Shamil Asgarli , Chi Hoi Yip

引用次数: 0

On Bruen chains 关于布鲁恩链条

IF 1.2 3区数学

Finite Fields and Their Applications Pub Date : 2024-08-14 DOI: 10.1016/j.ffa.2024.102491

John Bamberg , Jesse Lansdown , Geertrui Van de Voorde

引用次数: 0

Design of concatenative complete complementary codes for CCC-CDMA via specific sequences and extended Boolean functions 通过特定序列和扩展布尔函数为 CCC-CDMA 设计串联完整互补码

IF 1.2 3区数学

Finite Fields and Their Applications Pub Date : 2024-08-13 DOI: 10.1016/j.ffa.2024.102489

Rong Luo , Bingsheng Shen , Yang Yang , Zhengchun Zhou

{"title":"Design of concatenative complete complementary codes for CCC-CDMA via specific sequences and extended Boolean functions","authors":"Rong Luo , Bingsheng Shen , Yang Yang , Zhengchun Zhou","doi":"10.1016/j.ffa.2024.102489","DOIUrl":"10.1016/j.ffa.2024.102489","url":null,"abstract":"<div>A complete complementary code (CCC) consists of M sequence sets with size M. The sum of the auto-correlation functions of each sequence set is an impulse function, and the sum of cross-correlation functions of the different sequence sets is equal to zero. Thanks to their excellent correlation, CCCs received extensive use in engineering. In addition, they are strongly connected to orthogonal matrices. In some application scenarios, additional requirements are made for CCCs, such as recently proposed for concatenative CCC (CCCC) division multiple access (CCC-CDMA) technologies. In fact, CCCCs are a special kind of CCCs which requires that each sequence set in CCC be concatenated to form a zero-correlation-zone (ZCZ) sequence set. However, this requirement is challenging, and the literature is thin since there is only one construction in this context. We propose to go beyond the literature through this contribution to reduce the gap between their interest and our limited knowledge of CCCCs. This paper will employ novel methods for designing CCCCs and precisely derive two constructions of these objects. The first is based on perfect cross Z-complementary pair and Hadamard matrices, and the second relies on extended Boolean functions. Specifically, we highlight that optimal and asymptotic optimal CCCCs could be obtained through the proposed constructions. Besides, we shall present a comparison analysis with former structures in the literature and examples to illustrate our main results.</div>","PeriodicalId":50446,"journal":{"name":"Finite Fields and Their Applications","volume":"99 ","pages":"Article 102489"},"PeriodicalIF":1.2,"publicationDate":"2024-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141978745","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

Designs with a simple automorphism group 具有简单自变群的设计

IF 1.2 3区数学

Finite Fields and Their Applications Pub Date : 2024-08-09 DOI: 10.1016/j.ffa.2024.102488

Alessandro Montinaro , Yanwei Zhao , Zhilin Zhang , Shenglin Zhou

引用次数: 0