Advances in Mathematics of Communications最新文献

{"title":"New classes of nearly optimal time-hopping sequence sets for UWB systems","authors":"Peihua Li, Xingyu Zheng, Cuiling Fan","doi":"10.3934/amc.2023018","DOIUrl":"https://doi.org/10.3934/amc.2023018","url":null,"abstract":"","PeriodicalId":50859,"journal":{"name":"Advances in Mathematics of Communications","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72624354","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Constructions of irredundant orthogonal arrays","authors":"Guangzhou Chen, Xiaotong Zhang","doi":"10.3934/amc.2021051","DOIUrl":"https://doi.org/10.3934/amc.2021051","url":null,"abstract":"<p style='text-indent:20px;'>An <inline-formula><tex-math id=\"M1\">begin{document}$ N times k $end{document}</tex-math></inline-formula> array <inline-formula><tex-math id=\"M2\">begin{document}$ A $end{document}</tex-math></inline-formula> with entries from <inline-formula><tex-math id=\"M3\">begin{document}$ v $end{document}</tex-math></inline-formula>-set <inline-formula><tex-math id=\"M4\">begin{document}$ mathcal{V} $end{document}</tex-math></inline-formula> is said to be an <i>orthogonal array</i> with <inline-formula><tex-math id=\"M5\">begin{document}$ v $end{document}</tex-math></inline-formula> levels, strength <inline-formula><tex-math id=\"M6\">begin{document}$ t $end{document}</tex-math></inline-formula> and index <inline-formula><tex-math id=\"M7\">begin{document}$ lambda $end{document}</tex-math></inline-formula>, denoted by OA<inline-formula><tex-math id=\"M8\">begin{document}$ (N,k,v,t) $end{document}</tex-math></inline-formula>, if every <inline-formula><tex-math id=\"M9\">begin{document}$ Ntimes t $end{document}</tex-math></inline-formula> sub-array of <inline-formula><tex-math id=\"M10\">begin{document}$ A $end{document}</tex-math></inline-formula> contains each <inline-formula><tex-math id=\"M11\">begin{document}$ t $end{document}</tex-math></inline-formula>-tuple based on <inline-formula><tex-math id=\"M12\">begin{document}$ mathcal{V} $end{document}</tex-math></inline-formula> exactly <inline-formula><tex-math id=\"M13\">begin{document}$ lambda $end{document}</tex-math></inline-formula> times as a row. An OA<inline-formula><tex-math id=\"M14\">begin{document}$ (N,k,v,t) $end{document}</tex-math></inline-formula> is called <i>irredundant</i>, denoted by IrOA<inline-formula><tex-math id=\"M15\">begin{document}$ (N,k,v,t) $end{document}</tex-math></inline-formula>, if in any <inline-formula><tex-math id=\"M16\">begin{document}$ Ntimes (k-t ) $end{document}</tex-math></inline-formula> sub-array, all of its rows are different. Goyeneche and <inline-formula><tex-math id=\"M17\">begin{document}$ dot{Z} $end{document}</tex-math></inline-formula>yczkowski firstly introduced the definition of an IrOA and showed that an IrOA<inline-formula><tex-math id=\"M18\">begin{document}$ (N,k,v,t) $end{document}</tex-math></inline-formula> corresponds to a <inline-formula><tex-math id=\"M19\">begin{document}$ t $end{document}</tex-math></inline-formula>-uniform state of <inline-formula><tex-math id=\"M20\">begin{document}$ k $end{document}</tex-math></inline-formula> subsystems with local dimension <inline-formula><tex-math id=\"M21\">begin{document}$ v $end{document}</tex-math></inline-formula> (Physical Review A. 90 (2014), 022316). In this paper, we present some new constructions of irredundant orthogonal arrays by using difference matrices and some special matrices over finite fields, respectively, as a consequence, many infinite families of irredundant orthogonal arrays are obtained. Furthermore, several infinite classes of <inline-formula><tex-math id=\"M22\">begin{document}$ t $en","PeriodicalId":50859,"journal":{"name":"Advances in Mathematics of Communications","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79439330","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A coercion-resistant blockchain-based E-voting protocol with receipts","authors":"Chiara Spadafora, Riccardo Longo, M. Sala","doi":"10.3934/AMC.2021005","DOIUrl":"https://doi.org/10.3934/AMC.2021005","url":null,"abstract":"We propose a decentralized e-voting protocol that is coercion-resistant and vote-selling resistant, while being also completely transparent and not receipt-free. We achieve decentralization using blockchain technology. Because of the properties such as transparency, decentralization, and non-repudiation, blockchain is a fundamental technology of great interest in its own right, and it also has large potential when integrated into many other areas. We prove the security of the protocol under the standard DDH assumption on the underlying prime-order cyclic group (e.g. the group of points of an elliptic curve), as well as under standard assumptions on blockchain robustness.","PeriodicalId":50859,"journal":{"name":"Advances in Mathematics of Communications","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72713615","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Five-weight codes from three-valued correlation of M-sequences","authors":"M. Shi, Liqin Qian, T. Helleseth, P. Solé","doi":"10.3934/amc.2021022","DOIUrl":"https://doi.org/10.3934/amc.2021022","url":null,"abstract":"<p style='text-indent:20px;'>In this paper, for each of six families of three-valued <inline-formula><tex-math id=\"M1\">begin{document}$ m $end{document}</tex-math></inline-formula>-sequence correlation, we construct an infinite family of five-weight codes from trace codes over the ring <inline-formula><tex-math id=\"M2\">begin{document}$ R = mathbb{F}_2+umathbb{F}_2 $end{document}</tex-math></inline-formula>, where <inline-formula><tex-math id=\"M3\">begin{document}$ u^2 = 0. $end{document}</tex-math></inline-formula> The trace codes have the algebraic structure of abelian codes. Their Lee weight distribution is computed by using character sums. Their support structure is determined. An application to secret sharing schemes is given. The parameters of the binary image are <inline-formula><tex-math id=\"M4\">begin{document}$ [2^{m+1}(2^m-1),4m,2^{m}(2^m-2^r)] $end{document}</tex-math></inline-formula> for some explicit <inline-formula><tex-math id=\"M5\">begin{document}$ r. $end{document}</tex-math></inline-formula></p>","PeriodicalId":50859,"journal":{"name":"Advances in Mathematics of Communications","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91397712","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Tight security analysis of the public Permutation-based $ {{textsf{PMAC_Plus}}} $","authors":"Avijit Dutta, M. Nandi, Suprita Talnikar","doi":"10.3934/amc.2023025","DOIUrl":"https://doi.org/10.3934/amc.2023025","url":null,"abstract":"","PeriodicalId":50859,"journal":{"name":"Advances in Mathematics of Communications","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90000371","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Some invariants related to threshold and chain graphs","authors":"R. Raja, Samir Ahmad Wagay","doi":"10.3934/amc.2023020","DOIUrl":"https://doi.org/10.3934/amc.2023020","url":null,"abstract":"","PeriodicalId":50859,"journal":{"name":"Advances in Mathematics of Communications","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87321439","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Some progress on optimal $ 2 $-D $ (ntimes m,3,2,1) $-optical orthogonal codes","authors":"Kailu Yang, Xiaomiao Wang, Menglong Zhang, Lidong Wang","doi":"10.3934/AMC.2021012","DOIUrl":"https://doi.org/10.3934/AMC.2021012","url":null,"abstract":"In this paper, we are concerned about bounds and constructions of optimal begin{document}$ 2 $end{document} -D begin{document}$ (ntimes m,3,2,1) $end{document} -optical orthogonal codes. The exact number of codewords of an optimal begin{document}$ 2 $end{document} -D begin{document}$ (ntimes m,3,2,1) $end{document} -optical orthogonal code is determined for begin{document}$ n = 2 $end{document} , begin{document}$ mequiv 1 pmod{2} $end{document} , and begin{document}$ nequiv 1 pmod{2} $end{document} , begin{document}$ mequiv 1,3,5 pmod{12} $end{document} , and begin{document}$ nequiv 4 pmod{6} $end{document} , begin{document}$ mequiv 8 pmod{16} $end{document} .","PeriodicalId":50859,"journal":{"name":"Advances in Mathematics of Communications","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86130061","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Equivalence for generalized Boolean functions","authors":"Ayça Çesmelioglu, W. Meidl","doi":"10.3934/amc.2023009","DOIUrl":"https://doi.org/10.3934/amc.2023009","url":null,"abstract":"","PeriodicalId":50859,"journal":{"name":"Advances in Mathematics of Communications","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76836648","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The weight recursions for the 2-rotation symmetric quartic Boolean functions","authors":"T. Cusick, Younhwan Cheon","doi":"10.3934/AMC.2021011","DOIUrl":"https://doi.org/10.3934/AMC.2021011","url":null,"abstract":"A Boolean function in begin{document}$ n $end{document} variables is 2-rotation symmetric if it is invariant under even powers of begin{document}$ rho(x_1, ldots, x_n) = (x_2, ldots, x_n, x_1) $end{document} , but not under the first power (ordinary rotation symmetry); we call such a function a 2-function. A 2-function is called monomial rotation symmetric (MRS) if it is generated by applying powers of begin{document}$ rho^2 $end{document} to a single monomial. If the quartic MRS 2-function in begin{document}$ 2n $end{document} variables has a monomial begin{document}$ x_1 x_q x_r x_s $end{document} , then we use the notation begin{document}$ {2-}(1,q,r,s)_{2n} $end{document} for the function. A detailed theory of equivalence of quartic MRS 2-functions in begin{document}$ 2n $end{document} variables was given in a begin{document}$ 2020 $end{document} paper by Cusick, Cheon and Dougan. This theory divides naturally into two classes, called begin{document}$ mf1 $end{document} and begin{document}$ mf2 $end{document} in the paper. After describing the equivalence classes, the second major problem is giving details of the linear recursions that the Hamming weights for any sequence of functions begin{document}$ {2-}(1,q,r,s)_{2n} $end{document} (with begin{document}$ q say), begin{document}$ n = s, s+1, ldots $end{document} can be shown to satisfy. This problem was solved for the begin{document}$ mf1 $end{document} case only in the begin{document}$ 2020 $end{document} paper. Using new ideas about \"short\" functions, Cusick and Cheon found formulas for the begin{document}$ mf2 $end{document} weights in a begin{document}$ 2021 $end{document} sequel to the begin{document}$ 2020 $end{document} paper. In this paper the actual recursions for the weights in the begin{document}$ mf2 $end{document} case are determined.","PeriodicalId":50859,"journal":{"name":"Advances in Mathematics of Communications","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78042776","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Quantum states associated to mixed graphs and their algebraic characterization","authors":"Constanza Riera, M. Parker, P. Stănică","doi":"10.3934/AMC.2021015","DOIUrl":"https://doi.org/10.3934/AMC.2021015","url":null,"abstract":"Graph states are present in quantum information and found applications ranging from quantum network protocols (like secret sharing) to measurement based quantum computing. In this paper, we extend the notion of graph states, which can be regarded as pure quantum graph states, or as homogeneous quadratic Boolean functions associated to simple undirected graphs, to quantum states based on mixed graphs (graphs which allow both directed and undirected edges), obtaining mixed quantum states, which are defined by matrices associated to the measurement of homogeneous quadratic Boolean functions in some (ancillary) variables. In our main result, we describe the extended graph state as the sum of terms of a commutative subgroup of the stabilizer group of the corresponding mixed graph with the edges' directions reversed.","PeriodicalId":50859,"journal":{"name":"Advances in Mathematics of Communications","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84538118","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}