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New classes of nearly optimal time-hopping sequence sets for UWB systems 一类新的超宽带系统近最优跳时序列集
IF 0.9 4区 计算机科学
Advances in Mathematics of Communications Pub Date : 2023-01-01 DOI: 10.3934/amc.2023018
Peihua Li, Xingyu Zheng, Cuiling Fan
{"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":"60 1","pages":""},"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}
引用次数: 0
A coercion-resistant blockchain-based E-voting protocol with receipts 一种带有收据的基于区块链的抗强制电子投票协议
IF 0.9 4区 计算机科学
Advances in Mathematics of Communications Pub Date : 2023-01-01 DOI: 10.3934/AMC.2021005
Chiara Spadafora, Riccardo Longo, M. Sala
{"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":"80 1","pages":"500-521"},"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}
引用次数: 4
Lee metrics on groups 李组度量
IF 0.9 4区 计算机科学
Advances in Mathematics of Communications Pub Date : 2022-06-09 DOI: 10.3934/amc.2023011
Ricardo A. Podest'a, Maximiliano G. Vides
{"title":"Lee metrics on groups","authors":"Ricardo A. Podest'a, Maximiliano G. Vides","doi":"10.3934/amc.2023011","DOIUrl":"https://doi.org/10.3934/amc.2023011","url":null,"abstract":"In this work we consider interval metrics on groups; that is, integral invariant metrics whose associated weight functions do not have gaps. We give conditions for a group to have and to have not interval metrics. Then we study Lee metrics on general groups, that is interval metrics having the finest unitary symmetric associated partition. These metrics generalize the classic Lee metric on cyclic groups. In the case that $G$ is a torsion-free group or a finite group of odd order, we prove that $G$ has a Lee metric if and only if $G$ is cyclic. Also, if $G$ is a group admitting Lee metrics then $G times mathbb{Z}_2^k$ always have Lee metrics for every $k in mathbb{N}$. Then, we show that some families of metacyclic groups, such as cyclic, dihedral, and dicyclic groups, always have Lee metrics. Finally, we give conditions for non-cyclic groups such that they do not have Lee metrics. We end with tables of all groups of order $le 31$ indicating which of them have (or have not) Lee metrics and why (not).","PeriodicalId":50859,"journal":{"name":"Advances in Mathematics of Communications","volume":"94 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2022-06-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91299998","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}
引用次数: 0
Weierstrass semigroups on the third function field in a tower attaining the Drinfeld-Vlăduţ bound 塔上第三函数域上的Weierstrass半群达到了drinfeld - vl<e:1>界
IF 0.9 4区 计算机科学
Advances in Mathematics of Communications Pub Date : 2022-01-01 DOI: 10.3934/amc.2022066
Shudi Yang, Chuangqiang Hu
{"title":"Weierstrass semigroups on the third function field in a tower attaining the Drinfeld-Vlăduţ bound","authors":"Shudi Yang, Chuangqiang Hu","doi":"10.3934/amc.2022066","DOIUrl":"https://doi.org/10.3934/amc.2022066","url":null,"abstract":"<p style='text-indent:20px;'>For applications in algebraic geometry codes, an explicit description of bases of the Riemann-Roch spaces over function fields is needed. We investigate the third function field <inline-formula><tex-math id=\"M1\">begin{document}$ F^{(3)} $end{document}</tex-math></inline-formula> in a tower of Artin-Schreier extensions described by Garcia and Stichtenoth reaching the Drinfeld-Vlăduţ bound. We construct new bases for the related Riemann-Roch spaces of <inline-formula><tex-math id=\"M2\">begin{document}$ F^{(3)} $end{document}</tex-math></inline-formula> and present some basic properties of divisors on a line. From the bases, we explicitly calculate the Weierstrass semigroups and pure gaps at several places on <inline-formula><tex-math id=\"M3\">begin{document}$ F^{(3)} $end{document}</tex-math></inline-formula>. All of these results can be viewed as a generalization of the previous work done by Voss and Høholdt (1997).</p>","PeriodicalId":50859,"journal":{"name":"Advances in Mathematics of Communications","volume":"6 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87408615","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}
引用次数: 1
Introduction to the special issue dedicated to Cunsheng Ding on the occasion of his 60th birthday 丁存生60大寿特刊简介
IF 0.9 4区 计算机科学
Advances in Mathematics of Communications Pub Date : 2022-01-01 DOI: 10.3934/amc.2022089
{"title":"Introduction to the special issue dedicated to Cunsheng Ding on the occasion of his 60th birthday","authors":"","doi":"10.3934/amc.2022089","DOIUrl":"https://doi.org/10.3934/amc.2022089","url":null,"abstract":"","PeriodicalId":50859,"journal":{"name":"Advances in Mathematics of Communications","volume":"26 1","pages":"667-670"},"PeriodicalIF":0.9,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73241741","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}
引用次数: 0
Reconstructing points of superelliptic curves over a prime finite field 素数有限域上超椭圆曲线点的重构
IF 0.9 4区 计算机科学
Advances in Mathematics of Communications Pub Date : 2022-01-01 DOI: 10.3934/amc.2022022
J. Gutierrez
{"title":"Reconstructing points of superelliptic curves over a prime finite field","authors":"J. Gutierrez","doi":"10.3934/amc.2022022","DOIUrl":"https://doi.org/10.3934/amc.2022022","url":null,"abstract":"<p style='text-indent:20px;'>Let <inline-formula><tex-math id=\"M1\">begin{document}$ p $end{document}</tex-math></inline-formula> be a prime and <inline-formula><tex-math id=\"M2\">begin{document}$ mathbb{F}_p $end{document}</tex-math></inline-formula> the finite field with <inline-formula><tex-math id=\"M3\">begin{document}$ p $end{document}</tex-math></inline-formula> elements. We show how, when given an superelliptic curve <inline-formula><tex-math id=\"M4\">begin{document}$ Y^n+f(X) in mathbb{F}_p[X,Y] $end{document}</tex-math></inline-formula> and an approximation to <inline-formula><tex-math id=\"M5\">begin{document}$ (v_0,v_1) in mathbb{F}_p^2 $end{document}</tex-math></inline-formula> such that <inline-formula><tex-math id=\"M6\">begin{document}$ v_1^n = -f(v_0) $end{document}</tex-math></inline-formula>, one can recover <inline-formula><tex-math id=\"M7\">begin{document}$ (v_0,v_1) $end{document}</tex-math></inline-formula> efficiently, if the approximation is good enough. As consequence we provide an upper bound on the number of roots of such bivariate polynomials where the roots have certain restrictions. The results has been motivated by the predictability problem for non-linear pseudorandom number generators and, other potential applications to cryptography.</p>","PeriodicalId":50859,"journal":{"name":"Advances in Mathematics of Communications","volume":"55 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72662037","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}
引用次数: 2
$ mathbb{Z}_{p^r}mathbb{Z}_{p^s}mathbb{Z}_{p^t} $-additive cyclic codes $ mathbb {Z} _ {p r ^} mathbb {Z} _ {p s ^} mathbb {Z} _ {p ^ t} $添加剂循环码
IF 0.9 4区 计算机科学
Advances in Mathematics of Communications Pub Date : 2022-01-01 DOI: 10.3934/amc.2022079
Raziyeh Molaei, K. Khashyarmanesh
{"title":"$ mathbb{Z}_{p^r}mathbb{Z}_{p^s}mathbb{Z}_{p^t} $-additive cyclic codes","authors":"Raziyeh Molaei, K. Khashyarmanesh","doi":"10.3934/amc.2022079","DOIUrl":"https://doi.org/10.3934/amc.2022079","url":null,"abstract":"<p style='text-indent:20px;'>Let <inline-formula><tex-math id=\"M3\">begin{document}$ p $end{document}</tex-math></inline-formula> be a prime number and <inline-formula><tex-math id=\"M4\">begin{document}$ r, s, t $end{document}</tex-math></inline-formula> be positive integers such that <inline-formula><tex-math id=\"M5\">begin{document}$ rle sle t $end{document}</tex-math></inline-formula>. A <inline-formula><tex-math id=\"M6\">begin{document}$ mathbb{Z}_{p^r}mathbb{Z}_{p^s}mathbb{Z}_{p^t} $end{document}</tex-math></inline-formula>-additive code is a <inline-formula><tex-math id=\"M7\">begin{document}$ mathbb{Z}_{p^t} $end{document}</tex-math></inline-formula>-submodule of <inline-formula><tex-math id=\"M8\">begin{document}$ mathbb{Z}_{p^r}^{alpha} times mathbb{Z}_{p^s}^{beta} times mathbb{Z}_{p^t}^{gamma} $end{document}</tex-math></inline-formula>, where <inline-formula><tex-math id=\"M9\">begin{document}$ alpha, beta, gamma $end{document}</tex-math></inline-formula> are positive integers. In this paper, we study <inline-formula><tex-math id=\"M10\">begin{document}$ mathbb{Z}_{p^r}mathbb{Z}_{p^s}mathbb{Z}_{p^t} $end{document}</tex-math></inline-formula>-additive cyclic codes. In fact, we show that these codes can be identified as submodules of the ring <inline-formula><tex-math id=\"M11\">begin{document}$ R = mathbb{Z}_{p^r}[x]/big<x^alpha-1big> times mathbb{Z}_{p^s}[x]/big<x^beta-1big> times mathbb{Z}_{p^t}[x]/big<x^gamma-1big> $end{document}</tex-math></inline-formula>. Furthermore, we determine the generator polynomials and minimum generating sets of this kind of codes. Moreover, we investigate their dual codes.</p>","PeriodicalId":50859,"journal":{"name":"Advances in Mathematics of Communications","volume":"11 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78895618","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}
引用次数: 1
Optimal wide-gap-zone frequency hopping sequences 最优宽间隙区跳频序列
IF 0.9 4区 计算机科学
Advances in Mathematics of Communications Pub Date : 2022-01-01 DOI: 10.3934/amc.2022097
Qin Shu, Hai Liu, Xing Liu, Yun-xiu Yang, Wendong Chen
{"title":"Optimal wide-gap-zone frequency hopping sequences","authors":"Qin Shu, Hai Liu, Xing Liu, Yun-xiu Yang, Wendong Chen","doi":"10.3934/amc.2022097","DOIUrl":"https://doi.org/10.3934/amc.2022097","url":null,"abstract":"","PeriodicalId":50859,"journal":{"name":"Advances in Mathematics of Communications","volume":"25 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81436872","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}
引用次数: 0
Improved lower bounds for self-dual codes over $ mathbb{F}_{11} $, $ mathbb{F}_{13} $, $ mathbb{F}_{17} $, $ mathbb{F}_{19} $ and $ mathbb{F}_{23} $ 改进了$ mathbb{F}_{11} $、$ mathbb{F}_{13} $、$ mathbb{F}_{17} $、$ mathbb{F}_{19} $和$ mathbb{F}_{23} $上的自对偶码的下界
IF 0.9 4区 计算机科学
Advances in Mathematics of Communications Pub Date : 2022-01-01 DOI: 10.3934/amc.2022083
T. Gulliver, M. Harada
{"title":"Improved lower bounds for self-dual codes over $ mathbb{F}_{11} $, $ mathbb{F}_{13} $, $ mathbb{F}_{17} $, $ mathbb{F}_{19} $ and $ mathbb{F}_{23} $","authors":"T. Gulliver, M. Harada","doi":"10.3934/amc.2022083","DOIUrl":"https://doi.org/10.3934/amc.2022083","url":null,"abstract":"<p style='text-indent:20px;'>We construct self-dual codes over <inline-formula><tex-math id=\"M6\">begin{document}$ mathbb{F}_{11} $end{document}</tex-math></inline-formula>, <inline-formula><tex-math id=\"M7\">begin{document}$ mathbb{F}_{13} $end{document}</tex-math></inline-formula>, <inline-formula><tex-math id=\"M8\">begin{document}$ mathbb{F}_{17} $end{document}</tex-math></inline-formula>, <inline-formula><tex-math id=\"M9\">begin{document}$ mathbb{F}_{19} $end{document}</tex-math></inline-formula> and <inline-formula><tex-math id=\"M10\">begin{document}$ mathbb{F}_{23} $end{document}</tex-math></inline-formula> which improve the previously known lower bounds on the largest minimum weights. In particular, the largest possible minimum weight among self-dual <inline-formula><tex-math id=\"M11\">begin{document}$ [n, n/2] $end{document}</tex-math></inline-formula> codes over <inline-formula><tex-math id=\"M12\">begin{document}$ mathbb{F}_{p} $end{document}</tex-math></inline-formula> is determined for <inline-formula><tex-math id=\"M13\">begin{document}$ (p, n) = (19, 24) $end{document}</tex-math></inline-formula> and <inline-formula><tex-math id=\"M14\">begin{document}$ (23, 28) $end{document}</tex-math></inline-formula>.</p>","PeriodicalId":50859,"journal":{"name":"Advances in Mathematics of Communications","volume":"25 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83277931","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Finding small roots for bivariate polynomials over the ring of integers 寻找整数环上二元多项式的小根
IF 0.9 4区 计算机科学
Advances in Mathematics of Communications Pub Date : 2022-01-01 DOI: 10.3934/amc.2022012
Jiseung Kim, Changmin Lee
{"title":"Finding small roots for bivariate polynomials over the ring of integers","authors":"Jiseung Kim, Changmin Lee","doi":"10.3934/amc.2022012","DOIUrl":"https://doi.org/10.3934/amc.2022012","url":null,"abstract":"<p style='text-indent:20px;'>In this paper, we propose the first heuristic algorithm for finding small roots for a bivariate equation modulo an ideal <inline-formula><tex-math id=\"M3\">begin{document}$ mathcal{I} $end{document}</tex-math></inline-formula> over the ring of integers <inline-formula><tex-math id=\"M4\">begin{document}$ mathcal{R} $end{document}</tex-math></inline-formula>. Existing algorithms for solving polynomial equations with size constraints only work for bivariate modular equations over integers, and univariate modular equation over number fields.</p><p style='text-indent:20px;'>Both previous algorithms use a relation between the short vector in a skillfully structured lattice and a size constrained solution. Our algorithm also follows this framework, but we additionally use a polynomial factoring algorithm over number fields to recover a 'ring' root of a bivariate polynomial equation.</p><p style='text-indent:20px;'>As a result, when an LLL algorithm is employed to find a short vector, we can recover all small roots of a bivariate polynomial modulo <inline-formula><tex-math id=\"M5\">begin{document}$ mathcal{I} $end{document}</tex-math></inline-formula> in polynomial time under some constraint.</p>","PeriodicalId":50859,"journal":{"name":"Advances in Mathematics of Communications","volume":"23 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82463560","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}
引用次数: 0
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