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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":"35 5","pages":"691 - 701"},"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":"35 5","pages":"683 - 690"},"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":"35 5","pages":"667 - 682"},"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":"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
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