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The 4-adic complexity of quaternary sequences with optimal odd-periodic autocorrelation magnitude 具有最佳奇周期自相关幅度的四元序列的四元复杂性
IF 0.7 4区 工程技术
Applicable Algebra in Engineering Communication and Computing Pub Date : 2024-03-04 DOI: 10.1007/s00200-024-00647-5
Xiaoyan Jing, Zhefeng Xu
{"title":"The 4-adic complexity of quaternary sequences with optimal odd-periodic autocorrelation magnitude","authors":"Xiaoyan Jing, Zhefeng Xu","doi":"10.1007/s00200-024-00647-5","DOIUrl":"https://doi.org/10.1007/s00200-024-00647-5","url":null,"abstract":"<p>Based on the inverse Gray mapping and sign alternation transform, a new family of quaternary sequences with optimal odd-periodic autocorrelation magnitude has been constructed by using the Legendre sequence pair, twin-prime sequence pair and GMW sequence pair. In this paper, we use the correlation properties of the Legendre sequence pair, twin-prime sequence pair and GMW sequence pair to determine the lower bound of 4-adic complexity of these quaternary sequences, as well as show that these quaternary sequences have large 4-adic complexity.</p>","PeriodicalId":50742,"journal":{"name":"Applicable Algebra in Engineering Communication and Computing","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140036315","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
Optimal constacyclic codes with minimum distance four 距离最小的最优常环码四
IF 0.7 4区 工程技术
Applicable Algebra in Engineering Communication and Computing Pub Date : 2024-02-27 DOI: 10.1007/s00200-024-00648-4
Yajing Zhou, Xiaoshan Kai, Zhonghua Sun
{"title":"Optimal constacyclic codes with minimum distance four","authors":"Yajing Zhou, Xiaoshan Kai, Zhonghua Sun","doi":"10.1007/s00200-024-00648-4","DOIUrl":"https://doi.org/10.1007/s00200-024-00648-4","url":null,"abstract":"<p>Let <span>(n=2(p^m-1)/(p-1))</span>, where <i>p</i> is an odd prime and <span>(m&gt;1)</span> is a positive integer. In this paper, we research optimal <i>p</i>-ary constacyclic codes with two zeros. Two classes of optimal <i>p</i>-ary <span>([n,n-2m,4])</span> constacyclic codes are presented by searching the solutions of certain congruence equations over <span>(mathbb {F}_{p^m})</span>. Four explicit constructions of optimal constacyclic codes with such parameters are provided. The dual codes of a subclass of these constacyclic codes are also investigated.</p>","PeriodicalId":50742,"journal":{"name":"Applicable Algebra in Engineering Communication and Computing","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139980866","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 differential spectra of involutions with low differential uniformity over finite fields with even characteristic 论偶数特征有限域上具有低微分均匀性的卷积的微分谱
IF 0.7 4区 工程技术
Applicable Algebra in Engineering Communication and Computing Pub Date : 2024-02-25 DOI: 10.1007/s00200-024-00646-6
Guoqiang Liu, Sha Jiang, Kangquan Li
{"title":"On differential spectra of involutions with low differential uniformity over finite fields with even characteristic","authors":"Guoqiang Liu, Sha Jiang, Kangquan Li","doi":"10.1007/s00200-024-00646-6","DOIUrl":"https://doi.org/10.1007/s00200-024-00646-6","url":null,"abstract":"<p>In this paper, we determine the differential spectra of two known classes of involutions with low differential uniformity over finite fields with even characteristic completely. The key point of our method is that we propose several new definitions called special and ordinary points. In addition, it is interesting that one of our differential spectra is relative to the well-known Kloosterman sum.</p>","PeriodicalId":50742,"journal":{"name":"Applicable Algebra in Engineering Communication and Computing","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139980880","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
Weighted product of point clouds and simplicial complexes 点云和简单复数的加权乘积
IF 0.7 4区 工程技术
Applicable Algebra in Engineering Communication and Computing Pub Date : 2024-02-09 DOI: 10.1007/s00200-024-00644-8
Archana Babu, Sunil Jacob John, Baiju Thankachan
{"title":"Weighted product of point clouds and simplicial complexes","authors":"Archana Babu, Sunil Jacob John, Baiju Thankachan","doi":"10.1007/s00200-024-00644-8","DOIUrl":"https://doi.org/10.1007/s00200-024-00644-8","url":null,"abstract":"<p>This paper extends the concept of weighted point clouds and weighted simplicial complexes by introducing product point clouds and product simplicial complexes within a commutative ring with unity. Within an integral domain, the introduction of a weighted product chain group, along with the induced product weighted homomorphism and weighted product boundary maps, leads to significant outcomes and findings. To explore the algebraic characteristics of a weighted product structure, we introduce the concept of weighted product homology. This homology considers the relationship of weights assigned to elements within the structure and their impact on the structure’s underlying algebraic properties.</p>","PeriodicalId":50742,"journal":{"name":"Applicable Algebra in Engineering Communication and Computing","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-02-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139767028","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
Weight hierarchies of a class of three-weight p-ary linear codes from inhomogeneous quadratic functions 来自非均质二次函数的一类三重 pary 线性编码的权重分层
IF 0.7 4区 工程技术
Applicable Algebra in Engineering Communication and Computing Pub Date : 2024-02-04 DOI: 10.1007/s00200-024-00645-7
Shupeng Hu, Fei Li, Xiumei Li
{"title":"Weight hierarchies of a class of three-weight p-ary linear codes from inhomogeneous quadratic functions","authors":"Shupeng Hu, Fei Li, Xiumei Li","doi":"10.1007/s00200-024-00645-7","DOIUrl":"https://doi.org/10.1007/s00200-024-00645-7","url":null,"abstract":"<p>The weight hierarchy of a linear code have been an important research topic in coding theory since Wei’s original work in 1991. In this paper, choosing <span>(D=Big {(x,y)in Big ({mathbb {F}}_{p^{s_1}}times {mathbb {F}}_{p^{s_2}}Big )Big backslash {(0,0)}: f(x)+text {Tr}_1^{s_2}(alpha y)=0Big })</span> as a defining set, where <span>(alpha in {mathbb {F}}_{p^{s_2}}^*)</span>, <i>f</i>(<i>x</i>) is a quadratic form over <span>({mathbb {F}}_{p^{s_1}})</span> with values in <span>({mathbb {F}}_p)</span> and <i>f</i>(<i>x</i>) can be non-degenerate or not, we construct a family of three-weight <i>p</i>-ary linear codes and determine their weight distributions and weight hierarchies completely. Most of the codes can be used in secret sharing schemes.</p>","PeriodicalId":50742,"journal":{"name":"Applicable Algebra in Engineering Communication and Computing","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-02-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139767042","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
In memoriam Kai-Uwe Schmidt 纪念凯-乌韦-施密特
IF 0.6 4区 工程技术
Applicable Algebra in Engineering Communication and Computing Pub Date : 2024-01-27 DOI: 10.1007/s00200-024-00643-9
Teo Mora
{"title":"In memoriam Kai-Uwe Schmidt","authors":"Teo Mora","doi":"10.1007/s00200-024-00643-9","DOIUrl":"10.1007/s00200-024-00643-9","url":null,"abstract":"","PeriodicalId":50742,"journal":{"name":"Applicable Algebra in Engineering Communication and Computing","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140492280","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
Linear complementary pairs of constacyclic n-D codes over a finite commutative ring 有限交换环上恒环 n-D 码的线性互补对
IF 0.7 4区 工程技术
Applicable Algebra in Engineering Communication and Computing Pub Date : 2024-01-19 DOI: 10.1007/s00200-023-00640-4
Ridhima Thakral, Sucheta Dutt, Ranjeet Sehmi
{"title":"Linear complementary pairs of constacyclic n-D codes over a finite commutative ring","authors":"Ridhima Thakral, Sucheta Dutt, Ranjeet Sehmi","doi":"10.1007/s00200-023-00640-4","DOIUrl":"https://doi.org/10.1007/s00200-023-00640-4","url":null,"abstract":"<p>In this paper, a necessary condition which is sufficient as well for a pair of constacyclic 2-D codes over a finite commutative ring <i>R</i> to be an LCP of codes has been obtained. Also, a characterization of non-trivial LCP of constacyclic 2-D codes over <i>R</i> has been given and total number of such codes has been determined. The above results on constacyclic 2-D codes have been extended to constacyclic 3-D codes over <i>R</i>. The obtained results readily extend to constacyclic n-D codes, <span>(n ge 3)</span>, over finite commutative rings. Furthermore, some results on existence of non-trivial LCP of constacyclic 2-D codes over a finite chain ring have been obtained in terms of its residue field.</p>","PeriodicalId":50742,"journal":{"name":"Applicable Algebra in Engineering Communication and Computing","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-01-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139496706","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 the classification of non-exceptional APN functions 关于非特殊 APN 功能的分类
IF 0.7 4区 工程技术
Applicable Algebra in Engineering Communication and Computing Pub Date : 2024-01-18 DOI: 10.1007/s00200-023-00642-2
Nurdagül Anbar, Tekgül Kalaycı, Nihal Yurdakul
{"title":"On the classification of non-exceptional APN functions","authors":"Nurdagül Anbar, Tekgül Kalaycı, Nihal Yurdakul","doi":"10.1007/s00200-023-00642-2","DOIUrl":"https://doi.org/10.1007/s00200-023-00642-2","url":null,"abstract":"<p>An almost perfect non-linear (APN) function over <span>(mathbb {F}_{2^n})</span> is called exceptional APN if it remains APN over infinitely many extensions of <span>(mathbb {F}_{2^n})</span>. Exceptional APN functions have attracted attention of many researchers in the last decades. While the classification of exceptional APN monomials has been done by Hernando and McGuire, it has been conjectured by Aubry, McGuire and Rodier that up to equivalence, the only exceptional APN functions are the Gold and the Kasami–Welch monomial functions. Since then, many partial results have been on classifying non-exceptional APN polynomials. In this paper, for the classification of the exceptional property of APN functions, we introduce a new method that uses techniques from curves over finite fields. Then, we apply the method with Eisenstein’s irreducibility criterion and Kummer’s theorem to obtain new non-exceptional APN functions.</p>","PeriodicalId":50742,"journal":{"name":"Applicable Algebra in Engineering Communication and Computing","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-01-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139497149","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
Low-rank parity-check codes over finite commutative rings 有限交换环上的低秩奇偶校验码
IF 0.7 4区 工程技术
Applicable Algebra in Engineering Communication and Computing Pub Date : 2024-01-07 DOI: 10.1007/s00200-023-00641-3
Hermann Tchatchiem Kamche, Hervé Talé Kalachi, Franck Rivel Kamwa Djomou, Emmanuel Fouotsa
{"title":"Low-rank parity-check codes over finite commutative rings","authors":"Hermann Tchatchiem Kamche, Hervé Talé Kalachi, Franck Rivel Kamwa Djomou, Emmanuel Fouotsa","doi":"10.1007/s00200-023-00641-3","DOIUrl":"https://doi.org/10.1007/s00200-023-00641-3","url":null,"abstract":"<p>Low-Rank Parity-Check (LRPC) codes are a class of rank metric codes that have many applications specifically in network coding and cryptography. Recently, LRPC codes have been extended to Galois rings which are a specific case of finite rings. In this paper, we first define LRPC codes over finite commutative local rings, which are bricks of finite rings, with an efficient decoder. We improve the theoretical bound of the failure probability of the decoder. Then, we extend the work to arbitrary finite commutative rings. Certain conditions are generally used to ensure the success of the decoder. Over finite fields, one of these conditions is to choose a prime number as the extension degree of the Galois field. We have shown that one can construct LRPC codes without this condition on the degree of Galois extension.</p>","PeriodicalId":50742,"journal":{"name":"Applicable Algebra in Engineering Communication and Computing","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-01-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139396930","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
Spectral analysis for signed social networks 签名社交网络的频谱分析
IF 0.7 4区 工程技术
Applicable Algebra in Engineering Communication and Computing Pub Date : 2023-12-30 DOI: 10.1007/s00200-023-00639-x
Anita Kumari Rao, Bableen Kaur, Sachin Somra, Deepa Sinha
{"title":"Spectral analysis for signed social networks","authors":"Anita Kumari Rao, Bableen Kaur, Sachin Somra, Deepa Sinha","doi":"10.1007/s00200-023-00639-x","DOIUrl":"https://doi.org/10.1007/s00200-023-00639-x","url":null,"abstract":"<p>In complex real-world networks, the relation among vertices (people) changes over time. Even with millions of vertices, adding new vertices or deleting a few previous ones can drastically change the network’s dynamics. The Iterated Local Transitivity model is a deterministic model based on the principle of transitivity and local interaction among people. The same has been extended to signed social networks. Let <span>(Sigma)</span> be a signed graph with underlying graph <span>(G = (V, E))</span> and a function <span>(sigma :Erightarrow {+,-})</span> assigning signs to the edges. We determine the relation between the characteristic polynomials of signed graph <span>(Sigma)</span> and the signed graph obtained from <span>(Sigma)</span> by adding (deleting) vertices or by adding (deleting) edges. Consequently, we present a recurrence relation for a characteristic polynomial of the Iterated Local Transitivity model for signed graphs.</p>","PeriodicalId":50742,"journal":{"name":"Applicable Algebra in Engineering Communication and Computing","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139062719","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
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