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Applicable Algebra in Engineering Communication and Computing最新文献

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Correction: Effective algorithm for computing Noetherian operators of zero‑dimensional ideals 修正:计算零维理想的诺瑟算子的有效算法
IF 0.7 4区 工程技术
Applicable Algebra in Engineering Communication and Computing Pub Date : 2022-08-30 DOI: 10.1007/s00200-022-00579-y
Katsusuke Nabeshima, Shinichi Tajima
{"title":"Correction: Effective algorithm for computing Noetherian operators of zero‑dimensional ideals","authors":"Katsusuke Nabeshima, Shinichi Tajima","doi":"10.1007/s00200-022-00579-y","DOIUrl":"10.1007/s00200-022-00579-y","url":null,"abstract":"","PeriodicalId":50742,"journal":{"name":"Applicable Algebra in Engineering Communication and Computing","volume":"33 6","pages":"901 - 901"},"PeriodicalIF":0.7,"publicationDate":"2022-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43666794","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 subtowers and supertowers of recursive towers of function fields 函数域递归塔的子塔和超级塔的注释
IF 0.7 4区 工程技术
Applicable Algebra in Engineering Communication and Computing Pub Date : 2022-08-20 DOI: 10.1007/s00200-022-00576-1
M. Chara, H. Navarro, R. Toledano
{"title":"A note on subtowers and supertowers of recursive towers of function fields","authors":"M. Chara,&nbsp;H. Navarro,&nbsp;R. Toledano","doi":"10.1007/s00200-022-00576-1","DOIUrl":"10.1007/s00200-022-00576-1","url":null,"abstract":"<div><p>In this paper we study the problem of constructing non-trivial subtowers and supertowers of recursive towers of function fields over finite fields.</p></div>","PeriodicalId":50742,"journal":{"name":"Applicable Algebra in Engineering Communication and Computing","volume":"34 6","pages":"1063 - 1078"},"PeriodicalIF":0.7,"publicationDate":"2022-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50038242","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
Subalgebras in K[x] of small codimension 小余维K[x]中的子代数
IF 0.7 4区 工程技术
Applicable Algebra in Engineering Communication and Computing Pub Date : 2022-08-20 DOI: 10.1007/s00200-022-00573-4
Rode Grönkvist, Erik Leffler, Anna Torstensson, Victor Ufnarovski
{"title":"Subalgebras in K[x] of small codimension","authors":"Rode Grönkvist,&nbsp;Erik Leffler,&nbsp;Anna Torstensson,&nbsp;Victor Ufnarovski","doi":"10.1007/s00200-022-00573-4","DOIUrl":"10.1007/s00200-022-00573-4","url":null,"abstract":"<div><p>We introduce the concept of subalgebra spectrum, <i>Sp</i>(<i>A</i>), for a subalgebra <i>A</i> of finite codimension in <span>(mathbb {K}[x])</span>. The spectrum is a finite subset of the underlying field. We also introduce a tool, the characteristic polynomial of <i>A</i>, which has the spectrum as its set of zeroes. The characteristic polynomial can be computed from the generators of <i>A</i>, thus allowing us to find the spectrum of an algebra given by generators. We proceed by using the spectrum to get descriptions of subalgebras of finite codimension. More precisely we show that <i>A</i> can be described by a set of conditions that each is either of the type <span>(f(alpha )=f(beta ))</span> for <span>(alpha ,beta)</span> in <i>Sp</i>(<i>A</i>) or of the type stating that some linear combination of derivatives of different orders evaluated in elements of <i>Sp</i>(<i>A</i>) equals zero. We use these types of conditions to, by an inductive process, find explicit descriptions of subalgebras of codimension up to three. These descriptions also include SAGBI bases for each family of subalgebras.</p></div>","PeriodicalId":50742,"journal":{"name":"Applicable Algebra in Engineering Communication and Computing","volume":"33 6","pages":"751 - 789"},"PeriodicalIF":0.7,"publicationDate":"2022-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00200-022-00573-4.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42481789","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
Two modifications for Loidreau’s code-based cryptosystem 洛伊德鲁密码系统的两处修改
IF 0.6 4区 工程技术
Applicable Algebra in Engineering Communication and Computing Pub Date : 2022-08-16 DOI: 10.1007/s00200-022-00577-0
Wenshuo Guo, Fang-Wei Fu
{"title":"Two modifications for Loidreau’s code-based cryptosystem","authors":"Wenshuo Guo,&nbsp;Fang-Wei Fu","doi":"10.1007/s00200-022-00577-0","DOIUrl":"10.1007/s00200-022-00577-0","url":null,"abstract":"<div><p>This paper presents two modifications for Loidreau’s cryptosystem, a rank metric-based cryptosystem constructed by using Gabidulin codes in the McEliece setting. Recently a polynomial-time key recovery attack was proposed to break this cryptosystem in some cases. To prevent this attack, we propose the use of subcodes to disguise the secret codes in Modification I. In Modification II, we choose a random matrix of low column rank to mix with the secret matrix. Our analysis shows that these two modifications can both resist the existing structural attacks. Furthermore, these modifications have a much more compact representation of public keys compared to Classic McEliece, which has been selected into the fourth round of the NIST-PQC project.</p></div>","PeriodicalId":50742,"journal":{"name":"Applicable Algebra in Engineering Communication and Computing","volume":"35 5","pages":"647 - 665"},"PeriodicalIF":0.6,"publicationDate":"2022-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81666988","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
Effective algorithm for computing Noetherian operators of zero-dimensional ideals 零维理想noether算子的有效计算算法
IF 0.7 4区 工程技术
Applicable Algebra in Engineering Communication and Computing Pub Date : 2022-08-08 DOI: 10.1007/s00200-022-00570-7
Katsusuke Nabeshima, Shinichi Tajima
{"title":"Effective algorithm for computing Noetherian operators of zero-dimensional ideals","authors":"Katsusuke Nabeshima,&nbsp;Shinichi Tajima","doi":"10.1007/s00200-022-00570-7","DOIUrl":"10.1007/s00200-022-00570-7","url":null,"abstract":"<div><p>We consider Noetherian operators in the context of symbolic computation. Upon utilizing the theory of holonomic <span>({mathcal D})</span>-modules, we present a new method for computing Noetherian operators associated to a zero-dimensional ideal. An effective algorithm that consists mainly of linear algebra techniques is proposed for computing them. Moreover, as applications, new computation methods of polynomial ideals are discussed by utilizing the Noetherian operators.</p></div>","PeriodicalId":50742,"journal":{"name":"Applicable Algebra in Engineering Communication and Computing","volume":"33 6","pages":"867 - 899"},"PeriodicalIF":0.7,"publicationDate":"2022-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44198290","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 cryptographic properties of cubic and splitting Boolean functions 关于三次和分裂布尔函数的密码学性质
IF 0.6 4区 工程技术
Applicable Algebra in Engineering Communication and Computing Pub Date : 2022-08-06 DOI: 10.1007/s00200-022-00575-2
Augustine Musukwa, Massimiliano Sala, Irene Villa, Marco Zaninelli
{"title":"On cryptographic properties of cubic and splitting Boolean functions","authors":"Augustine Musukwa,&nbsp;Massimiliano Sala,&nbsp;Irene Villa,&nbsp;Marco Zaninelli","doi":"10.1007/s00200-022-00575-2","DOIUrl":"10.1007/s00200-022-00575-2","url":null,"abstract":"<div><p>The weight, balancedness and nonlinearity are important properties of Boolean functions, but they can be difficult to determine in general. In this paper, we study how to compute them for two classes of functions where these problems are more tractable. In particular, we study functions of degree three and the so-called “splitting” functions. The latter are functions that can be written as the sum of two functions defined over disjoint sets of variables. We show how, for splitting functions, studying these properties reduces to the study of simpler functions. We provide then a procedure to compute the weight of a cubic Boolean function. We show computationally that, for a cubic Boolean function with limited number of terms, this procedure is on average significantly more efficient than some other methods.</p></div>","PeriodicalId":50742,"journal":{"name":"Applicable Algebra in Engineering Communication and Computing","volume":"35 5","pages":"629 - 645"},"PeriodicalIF":0.6,"publicationDate":"2022-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00200-022-00575-2.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42127920","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
Strong metric dimension in annihilating-ideal graph of commutative rings 交换环的湮灭理想图中的强度量维数
IF 0.6 4区 工程技术
Applicable Algebra in Engineering Communication and Computing Pub Date : 2022-08-01 DOI: 10.1007/s00200-022-00574-3
Mitra Jalali, Reza Nikandish
{"title":"Strong metric dimension in annihilating-ideal graph of commutative rings","authors":"Mitra Jalali,&nbsp;Reza Nikandish","doi":"10.1007/s00200-022-00574-3","DOIUrl":"10.1007/s00200-022-00574-3","url":null,"abstract":"<div><p>In this paper, using Gallai’s Theorem and the notion of strong resolving graph, we determine the strong metric dimension in annihilating-ideal graph of commutative rings. For reduced rings, an explicit formula is given and for non-reduced rings, under some conditions, strong metric dimension is computed.</p></div>","PeriodicalId":50742,"journal":{"name":"Applicable Algebra in Engineering Communication and Computing","volume":"35 5","pages":"615 - 627"},"PeriodicalIF":0.6,"publicationDate":"2022-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47121791","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 support t-designs of extremal Type III and IV codes 关于极值III和IV型码的支持t-设计
IF 0.6 4区 工程技术
Applicable Algebra in Engineering Communication and Computing Pub Date : 2022-07-20 DOI: 10.1007/s00200-022-00571-6
Tsuyoshi Miezaki, Hiroyuki Nakasora
{"title":"On the support t-designs of extremal Type III and IV codes","authors":"Tsuyoshi Miezaki,&nbsp;Hiroyuki Nakasora","doi":"10.1007/s00200-022-00571-6","DOIUrl":"10.1007/s00200-022-00571-6","url":null,"abstract":"<div><p>Let <i>C</i> be an extremal Type III or IV code and <span>(D_{w})</span> be the support design of <i>C</i> for weight <i>w</i>. We introduce the numbers, <span>(delta (C))</span> and <i>s</i>(<i>C</i>), as follows: <span>(delta (C))</span> is the largest integer <i>t</i> such that, for all weights, <span>(D_{w})</span> is a <i>t</i>-design; <i>s</i>(<i>C</i>) denotes the largest integer <i>t</i> such that <i>w</i> exists and <span>(D_{w})</span> is a <i>t</i>-design. Herein, we consider the possible values of <span>(delta (C))</span> and <i>s</i>(<i>C</i>).</p></div>","PeriodicalId":50742,"journal":{"name":"Applicable Algebra in Engineering Communication and Computing","volume":"35 5","pages":"591 - 613"},"PeriodicalIF":0.6,"publicationDate":"2022-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47484961","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
Maximum distance separable repeated-root constacyclic codes over (mathbb {F}_{2^m}+umathbb {F}_{2^m}) with respect to the Lee distance 相对于李氏距离，$$mathbb {F}_{2^m}+umathbb {F}_{2^m}$$上可分离重根恒环码的最大距离
IF 0.6 4区 工程技术
Applicable Algebra in Engineering Communication and Computing Pub Date : 2022-07-14 DOI: 10.1007/s00200-022-00568-1
Hai Q. Dinh, Pramod Kumar Kewat, Nilay Kumar Mondal
{"title":"Maximum distance separable repeated-root constacyclic codes over (mathbb {F}_{2^m}+umathbb {F}_{2^m}) with respect to the Lee distance","authors":"Hai Q. Dinh,&nbsp;Pramod Kumar Kewat,&nbsp;Nilay Kumar Mondal","doi":"10.1007/s00200-022-00568-1","DOIUrl":"10.1007/s00200-022-00568-1","url":null,"abstract":"<div><p>Maximum distance separable (MDS) codes have the highest possible error-correcting capability among codes with the same length and size. Let <span>(gamma )</span> be nonzero in <span>(mathbb {F}_{2^m}.)</span> We consider all cyclic and <span>((1+ugamma ))</span>-constacyclic codes of length <span>(2^s)</span> over <span>(mathbb {F}_{2^m}+umathbb {F}_{2^m})</span> with their Lee distance and investigate all the cases whether the corresponding Gray images are MDS by giving an analogue of the Singleton bound for codes over <span>(mathbb {F}_{2^m}+umathbb {F}_{2^m})</span> with the Lee distance through Gray map.</p></div>","PeriodicalId":50742,"journal":{"name":"Applicable Algebra in Engineering Communication and Computing","volume":"35 4","pages":"557 - 571"},"PeriodicalIF":0.6,"publicationDate":"2022-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47364548","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
WDVV equations: symbolic computations of Hamiltonian operators WDVV方程：哈密顿算子的符号计算
IF 0.7 4区 工程技术
Applicable Algebra in Engineering Communication and Computing Pub Date : 2022-07-14 DOI: 10.1007/s00200-022-00565-4
Jakub Vašíček, Raffaele Vitolo
{"title":"WDVV equations: symbolic computations of Hamiltonian operators","authors":"Jakub Vašíček,&nbsp;Raffaele Vitolo","doi":"10.1007/s00200-022-00565-4","DOIUrl":"10.1007/s00200-022-00565-4","url":null,"abstract":"<div><p>We describe software for symbolic computations that we developed in order to find Hamiltonian operators for Witten–Dijkgraaf–Verlinde–Verlinde (WDVV) equations, and verify their compatibility. The computation involves nonlocal (integro-differential) operators, for which specific canonical forms and algorithms have been used.</p></div>","PeriodicalId":50742,"journal":{"name":"Applicable Algebra in Engineering Communication and Computing","volume":"33 6","pages":"915 - 934"},"PeriodicalIF":0.7,"publicationDate":"2022-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00200-022-00565-4.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49642862","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
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