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Applicable Algebra in Engineering Communication and Computing最新文献

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Cellular structure of the Pommaret-Seiler resolution for quasi-stable ideals 准稳定理想的Pommaret-Seiler解析的元胞结构
IF 0.6 4区 工程技术
Applicable Algebra in Engineering Communication and Computing Pub Date : 2022-10-13 DOI: 10.1007/s00200-022-00584-1
Rodrigo Iglesias, Eduardo Sáenz-de-Cabezón
{"title":"Cellular structure of the Pommaret-Seiler resolution for quasi-stable ideals","authors":"Rodrigo Iglesias,&nbsp;Eduardo Sáenz-de-Cabezón","doi":"10.1007/s00200-022-00584-1","DOIUrl":"10.1007/s00200-022-00584-1","url":null,"abstract":"<div><p>We prove that the Pommaret-Seiler resolution for quasi-stable ideals is cellular and give a cellular structure for it. This shows that this resolution is a generalization of the well known Eliahou–Kervaire resolution for stable ideals in a deeper sense. We also prove that the Pommaret-Seiler resolution can be reduced to the minimal one via Discrete Morse Theory and provide a constructive algorithm to perform this reduction.</p></div>","PeriodicalId":50742,"journal":{"name":"Applicable Algebra in Engineering Communication and Computing","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44621313","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
Smooth cubic surfaces with 15 lines 具有15条线的光滑立方体曲面
IF 0.7 4区 工程技术
Applicable Algebra in Engineering Communication and Computing Pub Date : 2022-10-03 DOI: 10.1007/s00200-022-00582-3
Fatma Karaoglu
{"title":"Smooth cubic surfaces with 15 lines","authors":"Fatma Karaoglu","doi":"10.1007/s00200-022-00582-3","DOIUrl":"10.1007/s00200-022-00582-3","url":null,"abstract":"<div><p>In this paper, we consider smooth cubic surfaces with 15 lines. It is known that such surfaces can be generated by means of a double six with two pairs of Galois conjugate lines defined over the quadratic extension. The approach taken here is to consider the generation by means of a set of 9 lines defined over the field of coordinates. Eight lines arise from the double six, while the ninth is the diagonal line of the two pairs of Galois conjugate lines. This allows us to express all necessary equations and objects in terms of a set of four parameters over the coordinate field. As an application, we classify the smooth cubic surfaces with 15 lines over small finite fields by computer. All our results match with an enumerative formula recently found by Das.</p></div>","PeriodicalId":50742,"journal":{"name":"Applicable Algebra in Engineering Communication and Computing","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2022-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44685378","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
Constructions of low-hit-zone frequency hopping sequence sets from cyclic codes 循环码低命中区跳频序列集的构造
IF 0.6 4区 工程技术
Applicable Algebra in Engineering Communication and Computing Pub Date : 2022-09-19 DOI: 10.1007/s00200-022-00581-4
Cuiling Fan, Xiaoxiao Cui, Wei Su
{"title":"Constructions of low-hit-zone frequency hopping sequence sets from cyclic codes","authors":"Cuiling Fan,&nbsp;Xiaoxiao Cui,&nbsp;Wei Su","doi":"10.1007/s00200-022-00581-4","DOIUrl":"10.1007/s00200-022-00581-4","url":null,"abstract":"<div><p>Low-hit-zone frequency hopping sequence (LHZ-FHS) sets having optimal Hamming correlation are desirable in quasi-synchronous communication systems. In this paper, we first derive a new bound on maximum nontrivial Hamming correlation of LHZ-FHS sets from the famous Singleton bound in error correcting code literature, then obtain a general construction of LHZ-FHS sets from cyclic codes. Especially, two classes of LHZ-FHS sets meeting the new bound are constructed from punctured Reed-Solomon codes.</p></div>","PeriodicalId":50742,"journal":{"name":"Applicable Algebra in Engineering Communication and Computing","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41611120","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
Note on the dimension of Goppa codes 关于Goppa码的维度的注意事项
IF 0.6 4区 工程技术
Applicable Algebra in Engineering Communication and Computing Pub Date : 2022-09-14 DOI: 10.1007/s00200-022-00578-z
Xiaoshan Quan, Qin Yue
{"title":"Note on the dimension of Goppa codes","authors":"Xiaoshan Quan,&nbsp;Qin Yue","doi":"10.1007/s00200-022-00578-z","DOIUrl":"10.1007/s00200-022-00578-z","url":null,"abstract":"<div><p>Let <span>(Gamma (L, g))</span> be a Goppa code over <span>({mathbb {F}}_q)</span>, where <span>(Lsubset mathbb {F}_{q^{m}})</span> is a support and <span>(g(x)in mathbb {F}_{q^{m}}[x])</span> is a polynomial with <i>s</i> distinct roots in <span>({mathbb {F}}_{q^m})</span>. In [Couvreur A, Otmani A, Tillich JP (2014) New identities relating wild Goppa codes. Finite Field Appl 29: 178–197.], Couvreur at al. gave the bound: <span>(dim _{{mathbb {F}}_{q}}Gamma (L,g^e)-dim _{{mathbb {F}}_{q}}Gamma (L,g^{e+1})le s,)</span> where <span>(e=q^{m-1}+q^{m-2}+cdots +q)</span>. In this paper, we give the conditions such that <span>(dim _{{mathbb {F}}_{q}}Gamma (L,g^e)=dim _{{mathbb {F}}_{q}}Gamma (L,g^{e+1}))</span>.</p></div>","PeriodicalId":50742,"journal":{"name":"Applicable Algebra in Engineering Communication and Computing","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49036821","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
Balance, pattern distribution and linear complexity of M-ary sequences from Sidel’nikov sequences Sidel 'nikov序列M-ary序列的平衡、模式分布和线性复杂度
IF 0.6 4区 工程技术
Applicable Algebra in Engineering Communication and Computing Pub Date : 2022-09-07 DOI: 10.1007/s00200-022-00580-5
Huaning Liu, Yixin Ren
{"title":"Balance, pattern distribution and linear complexity of M-ary sequences from Sidel’nikov sequences","authors":"Huaning Liu,&nbsp;Yixin Ren","doi":"10.1007/s00200-022-00580-5","DOIUrl":"10.1007/s00200-022-00580-5","url":null,"abstract":"<div><p>Kim, Chung, No and Chung introduced new families of <i>M</i>-ary sequences by using Sidel’nikov sequences and the shift-and-add method. Chung, No and Chung constructed more families of <i>M</i>-ary sequences based on Sidel’nikov sequences and the shift-and-inverse method. In this paper we further study the balancedness of these sequences and show that they have asymptotical uniform pattern distributions under some assumptions on the parameters of the sequences. Linear complexity profiles of the sequences are also studied.</p></div>","PeriodicalId":50742,"journal":{"name":"Applicable Algebra in Engineering Communication and Computing","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41628421","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
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,&nbsp;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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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
Using algebraic geometry to reconstruct a darboux cyclide from a calibrated camera picture 利用代数几何从校准的相机图像重建达布克斯自行车
IF 0.7 4区 工程技术
Applicable Algebra in Engineering Communication and Computing Pub Date : 2022-08-10 DOI: 10.1007/s00200-023-00600-y
Eriola Hoxhaj, Jean Michel Menjanahary, J. Schicho
{"title":"Using algebraic geometry to reconstruct a darboux cyclide from a calibrated camera picture","authors":"Eriola Hoxhaj, Jean Michel Menjanahary, J. Schicho","doi":"10.1007/s00200-023-00600-y","DOIUrl":"https://doi.org/10.1007/s00200-023-00600-y","url":null,"abstract":"","PeriodicalId":50742,"journal":{"name":"Applicable Algebra in Engineering Communication and Computing","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2022-08-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42691999","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
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