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Constructions of mismatched binary periodic complementary pairs 错配二进制周期互补对的构造
IF 0.9 4区 计算机科学
Advances in Mathematics of Communications Pub Date : 2023-01-01 DOI: 10.3934/amc.2023006
Lina Shi, Ruibin Ren, Yang Yang
{"title":"Constructions of mismatched binary periodic complementary pairs","authors":"Lina Shi, Ruibin Ren, Yang Yang","doi":"10.3934/amc.2023006","DOIUrl":"https://doi.org/10.3934/amc.2023006","url":null,"abstract":"","PeriodicalId":50859,"journal":{"name":"Advances in Mathematics of Communications","volume":"94 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73053738","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
On some codes from rank 3 primitive actions of the simple Chevalley group $ G_2(q) $ 关于简单Chevalley群$ G_2(q) $ 3阶基元作用的一些码
IF 0.9 4区 计算机科学
Advances in Mathematics of Communications Pub Date : 2023-01-01 DOI: 10.3934/amc.2022016
Tung Le, B. Rodrigues
{"title":"On some codes from rank 3 primitive actions of the simple Chevalley group $ G_2(q) $","authors":"Tung Le, B. Rodrigues","doi":"10.3934/amc.2022016","DOIUrl":"https://doi.org/10.3934/amc.2022016","url":null,"abstract":"<p style='text-indent:20px;'>Let <inline-formula><tex-math id=\"M2\">begin{document}$ G_2(q) $end{document}</tex-math></inline-formula> be a Chevalley group of type <inline-formula><tex-math id=\"M3\">begin{document}$ G_2 $end{document}</tex-math></inline-formula> over a finite field <inline-formula><tex-math id=\"M4\">begin{document}$ mathbb{F}_q $end{document}</tex-math></inline-formula>. Considering the <inline-formula><tex-math id=\"M5\">begin{document}$ G_2(q) $end{document}</tex-math></inline-formula>-primitive action of rank <inline-formula><tex-math id=\"M6\">begin{document}$ 3 $end{document}</tex-math></inline-formula> on the set of <inline-formula><tex-math id=\"M7\">begin{document}$ frac{q^3(q^3-1)}{2} $end{document}</tex-math></inline-formula> hyperplanes of type <inline-formula><tex-math id=\"M8\">begin{document}$ O_{6}^{-}(q) $end{document}</tex-math></inline-formula> in the <inline-formula><tex-math id=\"M9\">begin{document}$ 7 $end{document}</tex-math></inline-formula>-dimensional orthogonal space <inline-formula><tex-math id=\"M10\">begin{document}$ {{rm{PG}}}(7, q) $end{document}</tex-math></inline-formula>, we study the designs, codes, and some related geometric structures. We obtained the main parameters of the codes, the full automorphism groups of these structures, and geometric descriptions of the classes of minimum weight codewords.</p>","PeriodicalId":50859,"journal":{"name":"Advances in Mathematics of Communications","volume":"52 1","pages":"207-226"},"PeriodicalIF":0.9,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81289202","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 new class of optimal wide-gap one-coincidence frequency-hopping sequence sets 一类新的最优宽间隙单符合跳频序列集
IF 0.9 4区 计算机科学
Advances in Mathematics of Communications Pub Date : 2023-01-01 DOI: 10.3934/AMC.2020131
Wenli Ren, Feng Wang
{"title":"A new class of optimal wide-gap one-coincidence frequency-hopping sequence sets","authors":"Wenli Ren, Feng Wang","doi":"10.3934/AMC.2020131","DOIUrl":"https://doi.org/10.3934/AMC.2020131","url":null,"abstract":"In this paper, we propose a new class of optimal one-coincidence FHS (OC-FHS) sets with respect to the Peng-Fan bounds, including prime sequence sets and HMC sequence sets as special cases. Thereafter, through investigating their properties, we determine all of the FHS distances in the OC-FHS set. Finally, for a given positive integer, we also propose a new class of wide-gap one-coincidence FHS (WG-OC-FHS) sets where the FHS gap is larger than the given positive integer. Moreover, such a WG-OC-FHS set is optimal with respect to the WG-Lempel-Greenberger bound and the WG-Peng-Fan bounds simultaneously.","PeriodicalId":50859,"journal":{"name":"Advances in Mathematics of Communications","volume":"9 1","pages":"342-352"},"PeriodicalIF":0.9,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73884356","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
Efficient keyword search on encrypted dynamic cloud data 对加密动态云数据的高效关键字搜索
IF 0.9 4区 计算机科学
Advances in Mathematics of Communications Pub Date : 2023-01-01 DOI: 10.3934/amc.2022101
Laltu Sardar, Binanda Sengupta, S. Ruj
{"title":"Efficient keyword search on encrypted dynamic cloud data","authors":"Laltu Sardar, Binanda Sengupta, S. Ruj","doi":"10.3934/amc.2022101","DOIUrl":"https://doi.org/10.3934/amc.2022101","url":null,"abstract":"","PeriodicalId":50859,"journal":{"name":"Advances in Mathematics of Communications","volume":"23 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76036087","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
Parameters of some BCH codes over $ mathbb{F}_q $ of length $ frac{q^m-1}{2} $ 长度为$ frac{q^m-1}{2} $的$ mathbb{F}_q $上的一些BCH码的参数
IF 0.9 4区 计算机科学
Advances in Mathematics of Communications Pub Date : 2023-01-01 DOI: 10.3934/amc.2023007
Liqi Wang, Di Lu, Shixin Zhu
{"title":"Parameters of some BCH codes over $ mathbb{F}_q $ of length $ frac{q^m-1}{2} $","authors":"Liqi Wang, Di Lu, Shixin Zhu","doi":"10.3934/amc.2023007","DOIUrl":"https://doi.org/10.3934/amc.2023007","url":null,"abstract":"","PeriodicalId":50859,"journal":{"name":"Advances in Mathematics of Communications","volume":"6 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73165496","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
Nonexistence of some four dimensional linear codes attaining the Griesmer bound 某些达到Griesmer界的四维线性码的不存在性
IF 0.9 4区 计算机科学
Advances in Mathematics of Communications Pub Date : 2023-01-01 DOI: 10.3934/amc.2023024
W. Ma, Jinquan Luo
{"title":"Nonexistence of some four dimensional linear codes attaining the Griesmer bound","authors":"W. Ma, Jinquan Luo","doi":"10.3934/amc.2023024","DOIUrl":"https://doi.org/10.3934/amc.2023024","url":null,"abstract":"","PeriodicalId":50859,"journal":{"name":"Advances in Mathematics of Communications","volume":"17 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82638415","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
Two pointsets in $ mathrm{PG}(2,q^n) $ and the associated codes $ mathm {PG}(2,q^n) $中的两个点集及其相关代码
IF 0.9 4区 计算机科学
Advances in Mathematics of Communications Pub Date : 2023-01-01 DOI: 10.3934/amc.2022006
V. Napolitano, O. Polverino, Paolo Santonastaso, Ferdinando Zullo
{"title":"Two pointsets in $ mathrm{PG}(2,q^n) $ and the associated codes","authors":"V. Napolitano, O. Polverino, Paolo Santonastaso, Ferdinando Zullo","doi":"10.3934/amc.2022006","DOIUrl":"https://doi.org/10.3934/amc.2022006","url":null,"abstract":"<p style='text-indent:20px;'>In this paper we consider two pointsets in <inline-formula><tex-math id=\"M2\">begin{document}$ mathrm{PG}(2,q^n) $end{document}</tex-math></inline-formula> arising from a linear set <inline-formula><tex-math id=\"M3\">begin{document}$ L $end{document}</tex-math></inline-formula> of rank <inline-formula><tex-math id=\"M4\">begin{document}$ n $end{document}</tex-math></inline-formula> contained in a line of <inline-formula><tex-math id=\"M5\">begin{document}$ mathrm{PG}(2,q^n) $end{document}</tex-math></inline-formula>: the first one is a linear blocking set of Rédei type, the second one extends the construction of translation KM-arcs. We point out that their intersections pattern with lines is related to the weight distribution of the considered linear set <inline-formula><tex-math id=\"M6\">begin{document}$ L $end{document}</tex-math></inline-formula>. We then consider the Hamming metric codes associated with both these constructions, for which we can completely describe their weight distributions. By choosing <inline-formula><tex-math id=\"M7\">begin{document}$ L $end{document}</tex-math></inline-formula> to be an <inline-formula><tex-math id=\"M8\">begin{document}$ {mathbb F}_{q} $end{document}</tex-math></inline-formula>-linear set with a <i>short</i> weight distribution, then the associated codes have <i>few weights</i>. We conclude the paper by providing a connection between the <inline-formula><tex-math id=\"M9\">begin{document}$ Gammamathrm{L} $end{document}</tex-math></inline-formula>-class of <inline-formula><tex-math id=\"M10\">begin{document}$ L $end{document}</tex-math></inline-formula> and the number of inequivalent codes we can construct starting from it.</p>","PeriodicalId":50859,"journal":{"name":"Advances in Mathematics of Communications","volume":"114 1","pages":"227-245"},"PeriodicalIF":0.9,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77722569","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
Asymptotically good generalized quasi-cyclic codes over finite chain rings 有限链环上渐近良好的广义拟循环码
4区 计算机科学
Advances in Mathematics of Communications Pub Date : 2023-01-01 DOI: 10.3934/amc.2023034
Xiangrui Meng, Jian Gao, Fang-Wei Fu
{"title":"Asymptotically good generalized quasi-cyclic codes over finite chain rings","authors":"Xiangrui Meng, Jian Gao, Fang-Wei Fu","doi":"10.3934/amc.2023034","DOIUrl":"https://doi.org/10.3934/amc.2023034","url":null,"abstract":"In this paper, we construct a class of generalized quasi-cyclic (GQC) codes with index $ ell $ over finite chain rings. Based on probabilistic arguments, we discuss asymptotic rates and relative distances of this class of codes. As a result, we show that GQC codes with index $ ell $ over finite chain rings are asymptotically good.","PeriodicalId":50859,"journal":{"name":"Advances in Mathematics of Communications","volume":"109 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135699007","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
Fractional non-norm elements for division algebras, and an application to Cyclic Learning with Errors 除法代数的分数阶非范数元及其在带误差循环学习中的应用
4区 计算机科学
Advances in Mathematics of Communications Pub Date : 2023-01-01 DOI: 10.3934/amc.2023043
Andrew Mendelsohn, Cong Ling
{"title":"Fractional non-norm elements for division algebras, and an application to Cyclic Learning with Errors","authors":"Andrew Mendelsohn, Cong Ling","doi":"10.3934/amc.2023043","DOIUrl":"https://doi.org/10.3934/amc.2023043","url":null,"abstract":"Given a cyclotomic field $ K $ and a finite Galois extension $ L $, we discuss the construction of unit-magnitude elements in $ K $ which are not in the image of the field norm map $ N_{L/K}(L^times) $. We observe that the construction of Elia, Sethuraman, and Kumar extends to all cyclotomic fields whose rings of integers are a principal ideal domain, a fact we have not seen appear elsewhere in the literature. We then prove a number of lemmas concerning non-norm elements, and extend the above results to hold for arbitrary cyclotomic ground fields. We give examples of towers of fields and corresponding non-norm elements in both instances. Finally, we apply this to cryptography, defining a novel variant of Learning with Errors, defined over cyclic division algebras with fractional unit-magnitude non-norm elements, and reduce lattice problems defined over ideals in maximal orders in such algebras to the search problem for this form of LWE.","PeriodicalId":50859,"journal":{"name":"Advances in Mathematics of Communications","volume":"27 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135212418","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
Dualities for codes over finite Abelian groups 有限阿贝尔群上码的对偶性
IF 0.9 4区 计算机科学
Advances in Mathematics of Communications Pub Date : 2023-01-01 DOI: 10.3934/amc.2023023
S. Dougherty
{"title":"Dualities for codes over finite Abelian groups","authors":"S. Dougherty","doi":"10.3934/amc.2023023","DOIUrl":"https://doi.org/10.3934/amc.2023023","url":null,"abstract":"","PeriodicalId":50859,"journal":{"name":"Advances in Mathematics of Communications","volume":"18 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73590351","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
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