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The automorphism group of projective norm graphs 投影范数图的自同构群
IF 0.6 4区 工程技术
Applicable Algebra in Engineering Communication and Computing Pub Date : 2023-01-10 DOI: 10.1007/s00200-022-00590-3
Tomas Bayer, Tamás Mészáros, Lajos Rónyai, Tibor Szabó
{"title":"The automorphism group of projective norm graphs","authors":"Tomas Bayer,&nbsp;Tamás Mészáros,&nbsp;Lajos Rónyai,&nbsp;Tibor Szabó","doi":"10.1007/s00200-022-00590-3","DOIUrl":"10.1007/s00200-022-00590-3","url":null,"abstract":"<div><p>The projective norm graphs are central objects to extremal combinatorics. They appear in a variety of contexts, most importantly they provide tight constructions for the Turán number of complete bipartite graphs <span>(K_{t,s})</span> with <span>(s&gt;(t-1)!)</span>. In this note we deepen their understanding further by determining their automorphism group.\u0000</p></div>","PeriodicalId":50742,"journal":{"name":"Applicable Algebra in Engineering Communication and Computing","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2023-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00200-022-00590-3.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45591908","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Bounds on the maximum nonlinearity of permutations on the rings ({mathbb {Z}}_p) and ({mathbb {Z}}_{2p}) 环$$｛mathbb｛Z｝｝_p$$Zp上置换的最大非线性的界$
IF 0.6 4区 工程技术
Applicable Algebra in Engineering Communication and Computing Pub Date : 2023-01-04 DOI: 10.1007/s00200-022-00594-z
Prachi Gupta, P. R. Mishra, Atul Gaur
{"title":"Bounds on the maximum nonlinearity of permutations on the rings ({mathbb {Z}}_p) and ({mathbb {Z}}_{2p})","authors":"Prachi Gupta,&nbsp;P. R. Mishra,&nbsp;Atul Gaur","doi":"10.1007/s00200-022-00594-z","DOIUrl":"10.1007/s00200-022-00594-z","url":null,"abstract":"<div><p>In 2016, Y. Kumar et al. in the paper ‘<i>Affine equivalence and non-linearity of permutations over</i> <span>({mathbb {Z}}_n)</span>’ conjectured that: <i>For</i> <span>(nge 3)</span>, <i>the nonlinearity of any permutation on</i> <span>({mathbb {Z}}_n)</span>, <i>the ring of integers modulo</i> <i>n</i>, <i>cannot exceed</i> <span>(n-2)</span>. For an odd prime <i>p</i>, we settle the above conjecture when <span>(n=2p)</span> and for <span>(pequiv 3 pmod {4})</span> we prove the above conjecture with an improved upper bound. Further, we derive a lower bound on <span>(max {mathcal {N}}{mathcal {L}}_n)</span> when <i>n</i> is an odd prime or twice of an odd prime where <span>(max {mathcal {N}}{mathcal {L}}_n)</span> denotes the maximum possible nonlinearity of any permutation on <span>({mathbb {Z}}_n)</span>.</p></div>","PeriodicalId":50742,"journal":{"name":"Applicable Algebra in Engineering Communication and Computing","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2023-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49231409","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
Self-orthogonal codes constructed from weakly self-orthogonal designs invariant under an action of $$M_{11}$$ M 11 在$$M_{11}$$ m11的作用下，由弱自正交设计不变量构造自正交码
IF 0.7 4区 工程技术
Applicable Algebra in Engineering Communication and Computing Pub Date : 2023-01-01 DOI: 10.1007/s00200-020-00484-2
Vedrana Mikulić Crnković, Ivona Traunkar
{"title":"Self-orthogonal codes constructed from weakly self-orthogonal designs invariant under an action of \u0000 \u0000 \u0000 \u0000 $$M_{11}$$\u0000 \u0000 \u0000 M\u0000 11\u0000 \u0000 \u0000","authors":"Vedrana Mikulić Crnković, Ivona Traunkar","doi":"10.1007/s00200-020-00484-2","DOIUrl":"https://doi.org/10.1007/s00200-020-00484-2","url":null,"abstract":"","PeriodicalId":50742,"journal":{"name":"Applicable Algebra in Engineering Communication and Computing","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s00200-020-00484-2","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"52020721","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: 1
Quaternary Hermitian self-dual codes of lengths 26, 32, 36, 38 and 40 from modifications of well-known circulant constructions 长度为 26、32、36、38 和 40 的四元赫米特自偶码，源自对著名环形结构的修改
IF 0.6 4区 工程技术
Applicable Algebra in Engineering Communication and Computing Pub Date : 2022-12-22 DOI: 10.1007/s00200-022-00589-w
Adam Michael Roberts
{"title":"Quaternary Hermitian self-dual codes of lengths 26, 32, 36, 38 and 40 from modifications of well-known circulant constructions","authors":"Adam Michael Roberts","doi":"10.1007/s00200-022-00589-w","DOIUrl":"10.1007/s00200-022-00589-w","url":null,"abstract":"<div><p>In this work, we give three new techniques for constructing Hermitian self-dual codes over commutative Frobenius rings with a non-trivial involutory automorphism using <span>(lambda)</span>-circulant matrices. The new constructions are derived as modifications of various well-known circulant constructions of self-dual codes. Applying these constructions together with the building-up construction, we construct many new best known quaternary Hermitian self-dual codes of lengths 26, 32, 36, 38 and 40.</p></div>","PeriodicalId":50742,"journal":{"name":"Applicable Algebra in Engineering Communication and Computing","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76378620","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 a special type of permutation rational functions 一类特殊的置换有理函数
IF 0.6 4区 工程技术
Applicable Algebra in Engineering Communication and Computing Pub Date : 2022-12-16 DOI: 10.1007/s00200-022-00592-1
Nurdagül Anbar
{"title":"On a special type of permutation rational functions","authors":"Nurdagül Anbar","doi":"10.1007/s00200-022-00592-1","DOIUrl":"10.1007/s00200-022-00592-1","url":null,"abstract":"<div><p>Let <i>p</i> be a prime and <i>n</i> be a positive integer. We consider rational functions <span>(f_b(X)=X+1/(X^p-X+b))</span> over <span>({mathbb {F}}_{p^n})</span> with <span>(textrm{Tr}(b)ne 0)</span>. In Hou and Sze (Finite Fields Appl 68, Paper No. 10175, 2020), it is shown that <span>(f_b(X))</span> is not a permutation for <span>(p&gt;3)</span> and <span>(nge 5)</span>, while it is for <span>(p=2,3)</span> and <span>(nge 1)</span>. It is conjectured that <span>(f_b(X))</span> is also not a permutation for <span>(p&gt;3)</span> and <span>(n=3,4)</span>, which was recently proved sufficiently large primes in Bartoli and Hou (Finite Fields Appl 76, Paper No. 101904, 2021). In this note, we give a new proof for the fact that <span>(f_b(X))</span> is not a permutation for <span>(p&gt;3)</span> and <span>(nge 5)</span>. With this proof, we also show the existence of many elements <span>(bin {mathbb {F}}_{p^n})</span> for which <span>(f_b(X))</span> is not a permutation for <span>(n=3,4)</span>.</p></div>","PeriodicalId":50742,"journal":{"name":"Applicable Algebra in Engineering Communication and Computing","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41795141","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
Absorbing homogeneous polynomials arising from rational homotopy theory and graph theory 吸收有理同伦论和图论中的齐次多项式
IF 0.6 4区 工程技术
Applicable Algebra in Engineering Communication and Computing Pub Date : 2022-12-14 DOI: 10.1007/s00200-022-00591-2
Mahmoud Benkhalifa
{"title":"Absorbing homogeneous polynomials arising from rational homotopy theory and graph theory","authors":"Mahmoud Benkhalifa","doi":"10.1007/s00200-022-00591-2","DOIUrl":"10.1007/s00200-022-00591-2","url":null,"abstract":"<div><p>An ideal <span>({{mathcal {I}}})</span> of <span>({mathbb {Q}}[x_1,dots ,x_n])</span> is said to be <i>m</i>-absorbing if any monomial of total degree <span>(p&gt;m)</span> belongs to <span>({{mathcal {I}}})</span> and if there is a monomial <i>M</i> of total degree <i>m</i> such that <span>(Mnot in {{mathcal {I}}}.)</span> Inspired by the fundamental work of Lechuga and Murillo (Topology 39:89–94, 2000) who established a connection between graph theory and rational homotopy theory, these paper aims to characterise the <i>m</i>-absorbing ideals of <span>({mathbb {Q}}[x_1,dots ,x_n])</span> generated by a family of complete homogeneous symmetric polynomials of the form <span>(P^{(k)}_{rs}=sum _{t=1}^{k}x^{k-t}_{r}x^{t-1}_{s})</span>, where <span>(kge 3.)</span></p></div>","PeriodicalId":50742,"journal":{"name":"Applicable Algebra in Engineering Communication and Computing","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48450025","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
Efficient computation of Riemann–Roch spaces for plane curves with ordinary singularities 具有一般奇异点的平面曲线的Riemann-Roch空间的有效计算
IF 0.6 4区 工程技术
Applicable Algebra in Engineering Communication and Computing Pub Date : 2022-12-01 DOI: 10.1007/s00200-022-00588-x
Simon Abelard, Alain Couvreur, Grégoire Lecerf
{"title":"Efficient computation of Riemann–Roch spaces for plane curves with ordinary singularities","authors":"Simon Abelard,&nbsp;Alain Couvreur,&nbsp;Grégoire Lecerf","doi":"10.1007/s00200-022-00588-x","DOIUrl":"10.1007/s00200-022-00588-x","url":null,"abstract":"<div><p>We revisit the seminal Brill–Noether algorithm for plane curves with ordinary singularities. Our new approach takes advantage of fast algorithms for polynomials and structured matrices. We design a new probabilistic algorithm of Las Vegas type that computes a Riemann–Roch space in expected sub-quadratic time.</p></div>","PeriodicalId":50742,"journal":{"name":"Applicable Algebra in Engineering Communication and Computing","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43656009","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
De Nugis Groebnerialium 6: Rump, Ufnarovski, Zacharias 来自Nugis Groebnerialium 6：伦普，乌夫纳罗夫斯基，扎卡里亚斯
IF 0.7 4区 工程技术
Applicable Algebra in Engineering Communication and Computing Pub Date : 2022-11-07 DOI: 10.1007/s00200-022-00583-2
Michela Ceria, Ferdinando Mora
{"title":"De Nugis Groebnerialium 6: Rump, Ufnarovski, Zacharias","authors":"Michela Ceria,&nbsp;Ferdinando Mora","doi":"10.1007/s00200-022-00583-2","DOIUrl":"10.1007/s00200-022-00583-2","url":null,"abstract":"<div><p>Moved by a question posed us by Wolfgang Rump, we investigate the Rump ideal <span>({mathbb {I}}(p^2-pq+qp)subset {mathbb {Z}}langle q,q^{-1}, prangle )</span> and we show, this way, the power of Zacharias representation.</p></div>","PeriodicalId":50742,"journal":{"name":"Applicable Algebra in Engineering Communication and Computing","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2022-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45808800","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: 1
Degröbnerization: a political manifesto Degröbnerization:政治宣言
IF 0.7 4区 工程技术
Applicable Algebra in Engineering Communication and Computing Pub Date : 2022-11-05 DOI: 10.1007/s00200-022-00586-z
Michela Ceria, Samuel Lundqvist, Teo Mora
{"title":"Degröbnerization: a political manifesto","authors":"Michela Ceria,&nbsp;Samuel Lundqvist,&nbsp;Teo Mora","doi":"10.1007/s00200-022-00586-z","DOIUrl":"10.1007/s00200-022-00586-z","url":null,"abstract":"<div><p>Computer Algebra relies heavily on the computation of Gröbner bases, and these computations are primarily performed by means of Buchberger’s algorithm. In this overview paper, we focus on methods avoiding the computational intensity associated to Buchberger’s algorithm and, in most cases, even avoiding the concept of Gröbner bases, in favour of methods relying on linear algebra and combinatorics.</p></div>","PeriodicalId":50742,"journal":{"name":"Applicable Algebra in Engineering Communication and Computing","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2022-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46032436","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: 3
On the existence of r-primitive pairs ((alpha ,f(alpha ))) in finite fields 有限域中r-原元对$$(alpha ,f(alpha ))$$的存在性
IF 0.6 4区 工程技术
Applicable Algebra in Engineering Communication and Computing Pub Date : 2022-11-01 DOI: 10.1007/s00200-022-00585-0
Hanglong Zhang, Xiwang Cao
{"title":"On the existence of r-primitive pairs ((alpha ,f(alpha ))) in finite fields","authors":"Hanglong Zhang,&nbsp;Xiwang Cao","doi":"10.1007/s00200-022-00585-0","DOIUrl":"10.1007/s00200-022-00585-0","url":null,"abstract":"<div><p>Let <i>r</i> be a divisor of <span>(q-1.)</span> An element <span>(alpha in {mathbb {F}}_{q})</span> is said to be <i>r</i>-primitive if ord<span>((alpha )=frac{q-1}{r})</span>. In this paper, we discuss the existence of <i>r</i>-primitive pairs <span>((alpha , f(alpha )))</span> where <span>(alpha in {mathbb {F}}_q)</span>, <i>f</i>(<i>x</i>) is a general rational function of degree sum <i>m</i> (degree sum is the sum of the degrees of numerator and denominator of <i>f</i>(<i>x</i>)) and the denominator of <i>f</i>(<i>x</i>) is square-free. Then we show that for any integer <span>(m&gt;0)</span>, there exists a positive constant <span>(B_{r,m})</span> such that if <span>(q&gt;B_{r,m})</span>, then such <i>r</i>-primitive pairs exist. In particular, we present a bound for <span>(B_{r,m})</span> with <span>(r=2)</span> and <span>(min {2,3,4,5,6})</span>, and provide some conditions on the existence of 2-primitive pairs.</p></div>","PeriodicalId":50742,"journal":{"name":"Applicable Algebra in Engineering Communication and Computing","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47911612","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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