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

Permutation polynomials of the form xrh(xq−1) over Fq2 with even characteristics

IF 1.2 3区数学

Finite Fields and Their Applications Pub Date : 2025-02-14 DOI: 10.1016/j.ffa.2025.102594

Amritanshu Rai, Rohit Gupta

引用次数: 0

Four families of q-ary self-orthogonal codes via the defining-set construction

IF 1.2 3区数学

Finite Fields and Their Applications Pub Date : 2025-02-13 DOI: 10.1016/j.ffa.2025.102586

Jiayuan Zhang, Xiaoshan Kai, Ping Li, Shixin Zhu

引用次数: 0

On the construction of nonbinary LCD quadratic residue and double quadratic residue codes

IF 1.2 3区数学

Finite Fields and Their Applications Pub Date : 2025-02-11 DOI: 10.1016/j.ffa.2025.102591

Arezoo Soufi Karbaski , Taher Abualrub , Irfan Siap , Hashem Bordbar

{"title":"On the construction of nonbinary LCD quadratic residue and double quadratic residue codes","authors":"Arezoo Soufi Karbaski , Taher Abualrub , Irfan Siap , Hashem Bordbar","doi":"10.1016/j.ffa.2025.102591","DOIUrl":"10.1016/j.ffa.2025.102591","url":null,"abstract":"<div><div>Linear complementary dual (LCD) codes are an important class of error-correcting codes because of their applications in many areas such as their applications in cryptography and secret sharing [1], [4], [7]. In this paper, we construct a large class of nonbinary LCD codes from the class of nonbinary quadratic residue (QR) codes and nonbinary double QR codes. We have also introduced the class of extended quasi quadratic residue (QQR) codes and construct self-orthogonal codes from these codes. As an application of our study, we have presented an optimal ternary self-orthogonal code of parameters <math><mo>[</mo><mn>24</mn><mo>,</mo><mn>6</mn><mo>,</mo><mn>12</mn><mo>]</mo></math>. We have also constructed examples of self-orthogonal codes with parameters <math><msub><mrow><mo>[</mo><mn>2</mn><mrow><mo>(</mo><mi>q</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow><mo>,</mo><mfrac><mrow><mi>q</mi><mo>+</mo><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac><mo>,</mo><mn>2</mn><mi>d</mi><mo>]</mo></mrow><mrow><mi>p</mi></mrow></msub></math> and also examples of LCD codes with parameters <math><msub><mrow><mo>[</mo><mn>2</mn><mi>q</mi><mo>,</mo><mfrac><mrow><mi>q</mi><mo>−</mo><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac><mo>,</mo><mn>2</mn><mi>d</mi><mo>]</mo></mrow><mrow><mi>p</mi></mrow></msub></math> and <math><msub><mrow><mo>[</mo><mn>2</mn><mi>q</mi><mo>,</mo><mfrac><mrow><mi>q</mi><mo>+</mo><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac><mo>,</mo><mn>2</mn><mi>d</mi><mo>]</mo></mrow><mrow><mi>p</mi></mrow></msub></math> over <math><msub><mrow><mi>F</mi></mrow><mrow><mi>p</mi></mrow></msub></math> for different values of primes p and q.</div></div>","PeriodicalId":50446,"journal":{"name":"Finite Fields and Their Applications","volume":"103 ","pages":"Article 102591"},"PeriodicalIF":1.2,"publicationDate":"2025-02-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143386537","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

Homogenization of binary linear codes and their applications

IF 1.2 3区数学

Finite Fields and Their Applications Pub Date : 2025-02-06 DOI: 10.1016/j.ffa.2025.102589

Jong Yoon Hyun , Nilay Kumar Mondal , Yoonjin Lee

引用次数: 0

New classes of optimal p-ary cyclic codes with minimum distance four

IF 1.2 3区数学

Finite Fields and Their Applications Pub Date : 2025-02-05 DOI: 10.1016/j.ffa.2025.102588

Zhengbang Zha , Lei Hu , Gaofei Wu

引用次数: 0

On matrix algebras isomorphic to finite fields and planar Dembowski-Ostrom monomials

IF 1.2 3区数学

Finite Fields and Their Applications Pub Date : 2025-02-05 DOI: 10.1016/j.ffa.2025.102590

Christof Beierle , Patrick Felke

引用次数: 0

New constructions of abelian non-cyclic orbit codes based on parabolic subgroups and tensor products

IF 1.2 3区数学

Finite Fields and Their Applications Pub Date : 2025-02-05 DOI: 10.1016/j.ffa.2025.102587

Soleyman Askary, Nader Biranvand, Farrokh Shirjian

{"title":"New constructions of abelian non-cyclic orbit codes based on parabolic subgroups and tensor products","authors":"Soleyman Askary, Nader Biranvand, Farrokh Shirjian","doi":"10.1016/j.ffa.2025.102587","DOIUrl":"10.1016/j.ffa.2025.102587","url":null,"abstract":"<div><div>Orbit codes, as special constant dimension subspace codes, have attracted much attention due to their applications for error correction in random network coding. They arise as orbits of a subspace of <math><msubsup><mrow><mi>F</mi></mrow><mrow><mi>q</mi></mrow><mrow><mi>n</mi></mrow></msubsup></math> under the action of some subgroup of the finite general linear group <math><msub><mrow><mi>GL</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>(</mo><mi>q</mi><mo>)</mo></math>. The main contribution of this paper is to propose new methods for constructing large non-cyclic orbit codes. First, using the subgroup structure of maximal subgroups of <math><msub><mrow><mi>GL</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>(</mo><mi>q</mi><mo>)</mo></math>, we propose a new construction of an abelian non-cyclic orbit codes of size <math><msup><mrow><mi>q</mi></mrow><mrow><mi>k</mi></mrow></msup></math> with <math><mi>k</mi><mo>≤</mo><mi>n</mi><mo>/</mo><mn>2</mn></math>. The proposed code is shown to be a partial spread which in many cases is close to the known maximum-size codes. Next, considering a larger framework, we introduce the notion of tensor product operation for subspace codes and explicitly determine the parameters of such product codes. The parameters of the constructions presented in this paper improve the constructions already obtained in [6] and [7].</div></div>","PeriodicalId":50446,"journal":{"name":"Finite Fields and Their Applications","volume":"103 ","pages":"Article 102587"},"PeriodicalIF":1.2,"publicationDate":"2025-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143140082","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

An analogue of Girstmair's formula in function fields

IF 1.2 3区数学

Finite Fields and Their Applications Pub Date : 2025-01-27 DOI: 10.1016/j.ffa.2025.102585

Daisuke Shiomi

{"title":"An analogue of Girstmair's formula in function fields","authors":"Daisuke Shiomi","doi":"10.1016/j.ffa.2025.102585","DOIUrl":"10.1016/j.ffa.2025.102585","url":null,"abstract":"<div><div>Suppose that p is an odd prime and <math><mi>g</mi><mo>></mo><mn>1</mn></math> is a primitive root modulo p. Let M be a number field contained in the p-th cyclotomic field. In 1994, Girstmair found a surprising relation between the relative class number of M and the digits of <math><mn>1</mn><mo>/</mo><mi>p</mi></math> in base g. In this paper, we consider an analogue of Girstmair's formula in function fields. Suppose that <math><mi>P</mi><mo>∈</mo><msub><mrow><mi>F</mi></mrow><mrow><mi>q</mi></mrow></msub><mo>[</mo><mi>T</mi><mo>]</mo></math> is monic irreducible and <math><mi>G</mi><mo>∈</mo><msub><mrow><mi>F</mi></mrow><mrow><mi>q</mi></mrow></msub><mo>[</mo><mi>T</mi><mo>]</mo></math> is a primitive root modulo P. Let L be a field extension of <math><msub><mrow><mi>F</mi></mrow><mrow><mi>q</mi></mrow></msub><mo>(</mo><mi>T</mi><mo>)</mo></math> which is contained in the P-th cyclotomic function field. Our goal is to give relations between the plus and minus parts of the divisor class number of L and the digits of <math><mn>1</mn><mo>/</mo><mi>P</mi></math> in base G.</div></div>","PeriodicalId":50446,"journal":{"name":"Finite Fields and Their Applications","volume":"103 ","pages":"Article 102585"},"PeriodicalIF":1.2,"publicationDate":"2025-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143140089","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

Fq-primitive points on varieties over finite fields

IF 1.2 3区数学

Finite Fields and Their Applications Pub Date : 2025-01-24 DOI: 10.1016/j.ffa.2025.102582

Soniya Takshak , Giorgos Kapetanakis , Rajendra Kumar Sharma

引用次数: 0

The distance function on Coxeter-like graphs and self-dual codes

IF 1.2 3区数学

Finite Fields and Their Applications Pub Date : 2025-01-24 DOI: 10.1016/j.ffa.2025.102580

Marko Orel , Draženka Višnjić

引用次数: 0