发布求助
文献互助 智能选刊 最新文献

Applicable Algebra in Engineering Communication and Computing最新文献

筛选
英文 中文
Doubly even self-orthogonal codes from quasi-symmetric designs 来自准对称设计的双偶数自正交码
IF 0.7 4区 工程技术
Applicable Algebra in Engineering Communication and Computing Pub Date : 2024-06-24 DOI: 10.1007/s00200-024-00664-4
Dean Crnković, Doris Dumičić Danilović, Ana Šumberac, Andrea Švob
{"title":"Doubly even self-orthogonal codes from quasi-symmetric designs","authors":"Dean Crnković, Doris Dumičić Danilović, Ana Šumberac, Andrea Švob","doi":"10.1007/s00200-024-00664-4","DOIUrl":"https://doi.org/10.1007/s00200-024-00664-4","url":null,"abstract":"<p>In this paper, we give a construction of doubly even self-orthogonal codes from quasi-symmetric designs. Especially, we study orbit matrices of quasi-symmetric designs and give a construction of doubly even self-orthogonal codes from orbit matrices of quasi-symmetric designs of Blokhuis–Haemers type.</p>","PeriodicalId":50742,"journal":{"name":"Applicable Algebra in Engineering Communication and Computing","volume":"84 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141500938","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Geometry of the minimum distance 最小距离的几何形状
IF 0.7 4区 工程技术
Applicable Algebra in Engineering Communication and Computing Pub Date : 2024-06-07 DOI: 10.1007/s00200-024-00659-1
John Pawlina, Ştefan O. Tohǎneanu
{"title":"Geometry of the minimum distance","authors":"John Pawlina, Ştefan O. Tohǎneanu","doi":"10.1007/s00200-024-00659-1","DOIUrl":"https://doi.org/10.1007/s00200-024-00659-1","url":null,"abstract":"<p>Let <span>({{mathbb {K}}})</span> be any field, let <span>(Xsubset {mathbb P}^{k-1})</span> be a set of <span>(n)</span> distinct <span>({{mathbb {K}}})</span>-rational points, and let <span>(age 1)</span> be an integer. In this paper we find lower bounds for the minimum distance <span>(d(X)_a)</span> of the evaluation code of order <span>(a)</span> associated to <span>(X)</span>. The first results use <span>(alpha (X))</span>, the initial degree of the defining ideal of <span>(X)</span>, and the bounds are true for any set <span>(X)</span>. In another result we use <span>(s(X))</span>, the minimum socle degree, to find a lower bound for the case when <span>(X)</span> is in general linear position. In both situations we improve and generalize known results.</p>","PeriodicalId":50742,"journal":{"name":"Applicable Algebra in Engineering Communication and Computing","volume":"138 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141551790","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Some results on the Hamming distances of cyclic codes 关于循环码汉明距离的一些结果
IF 0.7 4区 工程技术
Applicable Algebra in Engineering Communication and Computing Pub Date : 2024-05-30 DOI: 10.1007/s00200-024-00660-8
Guantao Pan, Lanqiang Li, Ziwen Cao, Fuyin Tian
{"title":"Some results on the Hamming distances of cyclic codes","authors":"Guantao Pan, Lanqiang Li, Ziwen Cao, Fuyin Tian","doi":"10.1007/s00200-024-00660-8","DOIUrl":"https://doi.org/10.1007/s00200-024-00660-8","url":null,"abstract":"<p>Cyclic codes over finite fields have been studied for decades due to their wide applicability in communication systems, consumer electronics, and data storage systems. Let <i>p</i> be an odd prime and let <i>s</i> and <i>m</i> be positive integers. In this paper, we first determine the Hamming distances of all cyclic codes of length 8 over <span>(F_q)</span>. Building upon this, we explicitly obtain the Hamming distances of all repeated-root cyclic codes of length <span>(8p^s)</span> over <span>(F_q)</span>. As an application, we give all maximum distance separable cyclic codes of length <span>(8p^s)</span>.</p>","PeriodicalId":50742,"journal":{"name":"Applicable Algebra in Engineering Communication and Computing","volume":"22 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141196315","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
New results of sparse permutation polynomials with trace functions over $$mathbb {F}_{q^n}$$ 在 $$mathbb {F}_{q^n}$ 上具有迹函数的稀疏置换多项式的新结果
IF 0.7 4区 工程技术
Applicable Algebra in Engineering Communication and Computing Pub Date : 2024-05-13 DOI: 10.1007/s00200-024-00658-2
Yan-Ping Wang, Zhengbang Zha
{"title":"New results of sparse permutation polynomials with trace functions over $$mathbb {F}_{q^n}$$","authors":"Yan-Ping Wang, Zhengbang Zha","doi":"10.1007/s00200-024-00658-2","DOIUrl":"https://doi.org/10.1007/s00200-024-00658-2","url":null,"abstract":"<p>Permutation polynomials with sparse forms over finite fields attract researchers’ great interest and have important applications in many areas of mathematics and engineering. In this paper, by investigating the exponents (<i>s</i>, <i>i</i>) and the coefficients <span>(a,bin mathbb {F}_{q}^{*})</span>, we present some new results of permutation polynomials of the form <span>(f(x)= ax^{q^i(q^{2}-q+1)} + bx^{s} + textrm{Tr}_{q^n/q}(x))</span> over <span>(mathbb {F}_{q^n})</span> (<span>(n=2)</span> or 3). The permutation property of the new results is given by studying the number of solutions of special equations over <span>(mathbb {F}_{q^n})</span>.</p>","PeriodicalId":50742,"journal":{"name":"Applicable Algebra in Engineering Communication and Computing","volume":"54 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140926985","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On circulant involutory and orthogonal MDS matrices over finite commutative rings 关于有限交换环上的循环非正交矩阵和正交 MDS 矩阵
IF 0.7 4区 工程技术
Applicable Algebra in Engineering Communication and Computing Pub Date : 2024-04-27 DOI: 10.1007/s00200-024-00656-4
Shakir Ali, Atif Ahmad Khan, Bhupendra Singh
{"title":"On circulant involutory and orthogonal MDS matrices over finite commutative rings","authors":"Shakir Ali, Atif Ahmad Khan, Bhupendra Singh","doi":"10.1007/s00200-024-00656-4","DOIUrl":"https://doi.org/10.1007/s00200-024-00656-4","url":null,"abstract":"<p>Let <span>(k&gt;1)</span> be a fixed integer. In Gupta and Ray (Cryptography and Communications 7: 257–287, 2015), proved the non existence of <span>(2^k times 2^k)</span> orthogonal circulant MDS matrices and involutory circulant MDS matrices over finite fields of characteristic 2. The main aim of this paper is to prove the non-existence of orthogonal circulant MDS matrices of order <span>(2^ktimes 2^k)</span> and involutory circulant MDS matrices of order <i>k</i> over finite commutative rings of characteristic 2. Precisely, we prove that any circulant orthogonal matrix of order <span>(2^k)</span> over finite commutative rings of characteristic 2 with identity is not a MDS matrix. Moreover, some related results are also discussed. Finally, we provide some examples to prove that the assumed restrictions on our main results are not superfluous.</p>","PeriodicalId":50742,"journal":{"name":"Applicable Algebra in Engineering Communication and Computing","volume":"146 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-04-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140812697","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Sparse polynomial interpolation: faster strategies over finite fields 稀疏多项式插值：有限域上的更快策略
IF 0.7 4区 工程技术
Applicable Algebra in Engineering Communication and Computing Pub Date : 2024-04-27 DOI: 10.1007/s00200-024-00655-5
Joris van der Hoeven, Grégoire Lecerf
{"title":"Sparse polynomial interpolation: faster strategies over finite fields","authors":"Joris van der Hoeven, Grégoire Lecerf","doi":"10.1007/s00200-024-00655-5","DOIUrl":"https://doi.org/10.1007/s00200-024-00655-5","url":null,"abstract":"<p>Consider a multivariate polynomial <span>(f in K [x_1, ldots , x_n])</span> over a field <i>K</i>, which is given through a black box capable of evaluating <i>f</i> at points in <span>(K^n)</span>, or possibly at points in <span>(A^n)</span> for any <i>K</i>-algebra <i>A</i>. The problem of sparse interpolation is to express <i>f</i> in its usual form with respect to the monomial basis. We analyze the complexity of various old and new algorithms for this task in terms of bounds <i>D</i> and <i>T</i> for the total degree of <i>f</i> and its number of terms. We mainly focus on the case when <i>K</i> is a finite field and explore possible speed-ups.</p>","PeriodicalId":50742,"journal":{"name":"Applicable Algebra in Engineering Communication and Computing","volume":"146 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-04-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140813078","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Solving systems of algebraic equations over finite commutative rings and applications 有限交换环上代数方程解法及其应用
IF 0.7 4区 工程技术
Applicable Algebra in Engineering Communication and Computing Pub Date : 2024-04-24 DOI: 10.1007/s00200-024-00652-8
Hermann Tchatchiem Kamche, Hervé Talé Kalachi
{"title":"Solving systems of algebraic equations over finite commutative rings and applications","authors":"Hermann Tchatchiem Kamche, Hervé Talé Kalachi","doi":"10.1007/s00200-024-00652-8","DOIUrl":"https://doi.org/10.1007/s00200-024-00652-8","url":null,"abstract":"<p>Several problems in algebraic geometry and coding theory over finite rings are modeled by systems of algebraic equations. Among these problems, we have the rank decoding problem, which is used in the construction of public-key cryptosystems. A finite chain ring is a finite ring admitting exactly one maximal ideal and every ideal being generated by one element. In 2004, Nechaev and Mikhailov proposed two methods for solving systems of polynomial equations over finite chain rings. These methods used solutions over the residue field to construct all solutions step by step. However, for some types of algebraic equations, one simply needs partial solutions. In this paper, we combine two existing approaches to show how Gröbner bases over finite chain rings can be used to solve systems of algebraic equations over finite commutative rings. Then, we use skew polynomials and Plücker coordinates to show that some algebraic approaches used to solve the rank decoding problem and the MinRank problem over finite fields can be extended to finite principal ideal rings.</p>","PeriodicalId":50742,"journal":{"name":"Applicable Algebra in Engineering Communication and Computing","volume":"18 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140798004","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Metric dimension and strong metric dimension in annihilator-ideal graphs 湮没者理想图中的度量维度和强度量维度
IF 0.7 4区 工程技术
Applicable Algebra in Engineering Communication and Computing Pub Date : 2024-04-20 DOI: 10.1007/s00200-024-00657-3
R. Shahriyari, R. Nikandish, A. Tehranian, H. Rasouli
{"title":"Metric dimension and strong metric dimension in annihilator-ideal graphs","authors":"R. Shahriyari, R. Nikandish, A. Tehranian, H. Rasouli","doi":"10.1007/s00200-024-00657-3","DOIUrl":"https://doi.org/10.1007/s00200-024-00657-3","url":null,"abstract":"<p>Let <i>R</i> be a commutative ring with identity and <i>A</i>(<i>R</i>) be the set of ideals with non-zero annihilator. The annihilator-ideal graph of <i>R</i> is defined as the graph <span>(mathrm{A_I}(R))</span> with the vertex set <span>(A(R)^*=A(R)setminus {0})</span> and two distinct vertices <i>L</i>, <i>K</i> are adjacent if and only if <span>(textrm{Ann}_R(K) cup textrm{Ann}_R(L))</span> is a proper subset of <span>(textrm{Ann}_R(KL))</span>. In this paper, we determine the metric dimension of <span>(mathrm{A_I}(R))</span>. Also, the twin-free clique number for <span>(mathrm{A_I}(R))</span> is computed and as an application the strong metric dimension in annihilator-ideal graphs is given.</p>","PeriodicalId":50742,"journal":{"name":"Applicable Algebra in Engineering Communication and Computing","volume":"60 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140623606","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A note on the Assmus–Mattson theorem for some ternary codes 关于某些三元码的阿斯穆斯-马特森定理的说明
IF 0.7 4区 工程技术
Applicable Algebra in Engineering Communication and Computing Pub Date : 2024-04-09 DOI: 10.1007/s00200-024-00654-6
Eiichi Bannai, Tsuyoshi Miezaki, Hiroyuki Nakasora
{"title":"A note on the Assmus–Mattson theorem for some ternary codes","authors":"Eiichi Bannai, Tsuyoshi Miezaki, Hiroyuki Nakasora","doi":"10.1007/s00200-024-00654-6","DOIUrl":"https://doi.org/10.1007/s00200-024-00654-6","url":null,"abstract":"<p>Let <i>C</i> be a two and three-weight ternary code. Furthermore, we assume that <span>(C_ell )</span> are <i>t</i>-designs for all <span>(ell )</span> by the Assmus–Mattson theorem. We show that <span>(t le 5)</span>. As a corollary, we provide a new characterization of the (extended) ternary Golay code.</p>","PeriodicalId":50742,"journal":{"name":"Applicable Algebra in Engineering Communication and Computing","volume":"72 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140603171","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Obtaining new classes of optimal linear codes by puncturing and shortening optimal cyclic codes 通过穿刺和缩短最优循环码获得最优线性码的新类别
IF 0.7 4区 工程技术
Applicable Algebra in Engineering Communication and Computing Pub Date : 2024-04-06 DOI: 10.1007/s00200-024-00653-7
Félix Hernández, Gerardo Vega
{"title":"Obtaining new classes of optimal linear codes by puncturing and shortening optimal cyclic codes","authors":"Félix Hernández, Gerardo Vega","doi":"10.1007/s00200-024-00653-7","DOIUrl":"https://doi.org/10.1007/s00200-024-00653-7","url":null,"abstract":"<p>In this paper we use the puncturing and shortening techniques on two already-known classes of optimal cyclic codes in order to obtain three new classes of optimal linear codes achieving the Griesmer bound. The weight distributions for these codes are settled. We also investigate their dual codes and show that they are either optimal or almost optimal with respect to the sphere-packing bound. Moreover, these duals contain classes of almost maximum distance separable codes which are shown to be proper for error detection. Further, some of the obtained optimal linear codes are suitable for constructing secret sharing schemes with nice access structures.</p>","PeriodicalId":50742,"journal":{"name":"Applicable Algebra in Engineering Communication and Computing","volume":"5 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-04-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140571164","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
首页 上一页 下一页 尾页
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整，为了账户安全，请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
请完成安全验证×
相关产品
×
本文献相关产品
联系我们：info@booksci.cn Book学术提供免费学术资源搜索服务，方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号：481959085
Book学术官方微信