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On BCH split metacyclic codes 关于BCH分裂元环码
IF 0.9 4区 计算机科学
Advances in Mathematics of Communications Pub Date : 2023-01-01 DOI: 10.3934/amc.2021045
Angelot Behajaina
{"title":"On BCH split metacyclic codes","authors":"Angelot Behajaina","doi":"10.3934/amc.2021045","DOIUrl":"https://doi.org/10.3934/amc.2021045","url":null,"abstract":"<p style='text-indent:20px;'>Recently, Borello and Jamous have investigated some lower bounds on the dimension and minimum distance for dihedral codes, in analogy with the theory of BCH codes. In this paper, we extend some of their results to split metacyclic codes, that is, codes over semidirect products of cyclic groups.</p>","PeriodicalId":50859,"journal":{"name":"Advances in Mathematics of Communications","volume":"15 1","pages":"1181-1195"},"PeriodicalIF":0.9,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82160454","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
Asymptotically good $ mathbb{Z}_{p}mathbb{Z}_{p}[u]/langle u^{t}rangle $-additive cyclic codes 渐近良$ mathbb{Z}_{p}mathbb{Z}_{p}[u]/langle u^{t}rangle $-可加循环码
IF 0.9 4区 计算机科学
Advances in Mathematics of Communications Pub Date : 2023-01-01 DOI: 10.3934/amc.2022087
Ting Yao, Heqian Xu, Yongsheng Tang, Shixin Zhu
{"title":"Asymptotically good $ mathbb{Z}_{p}mathbb{Z}_{p}[u]/langle u^{t}rangle $-additive cyclic codes","authors":"Ting Yao, Heqian Xu, Yongsheng Tang, Shixin Zhu","doi":"10.3934/amc.2022087","DOIUrl":"https://doi.org/10.3934/amc.2022087","url":null,"abstract":"","PeriodicalId":50859,"journal":{"name":"Advances in Mathematics of Communications","volume":"66 1","pages":"1290-1301"},"PeriodicalIF":0.9,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84589368","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Partial direct product difference sets and almost quaternary sequences 部分直积差分集与几乎四元序列
IF 0.9 4区 计算机科学
Advances in Mathematics of Communications Pub Date : 2023-01-01 DOI: 10.3934/AMC.2021010
Büsra Özden, Oğuz Yayla
{"title":"Partial direct product difference sets and almost quaternary sequences","authors":"Büsra Özden, Oğuz Yayla","doi":"10.3934/AMC.2021010","DOIUrl":"https://doi.org/10.3934/AMC.2021010","url":null,"abstract":"In this paper, we study the begin{document}$ m $end{document} -ary sequences with (non-consecutive) two zero-symbols and at most two distinct autocorrelation coefficients, which are known as almost begin{document}$ m $end{document} -ary nearly perfect sequences. We show that these sequences are equivalent to begin{document}$ ell $end{document} -partial direct product difference sets (PDPDS), then we extend known results on the sequences with two consecutive zero-symbols to non-consecutive case. Next, we study the notion of multipliers and orbit combination for begin{document}$ ell $end{document} -PDPDS. Finally, we present two construction methods for a family of almost quaternary sequences with at most two out-of-phase autocorrelation coefficients.","PeriodicalId":50859,"journal":{"name":"Advances in Mathematics of Communications","volume":"33 1","pages":"572-588"},"PeriodicalIF":0.9,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78899369","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
Constructions of rotation symmetric Bent functions and Bent idempotent functions 旋转对称弯曲函数和弯曲幂等函数的构造
IF 0.9 4区 计算机科学
Advances in Mathematics of Communications Pub Date : 2023-01-01 DOI: 10.3934/amc.2023022
Xiaoyan Chen, Sihong Su
{"title":"Constructions of rotation symmetric Bent functions and Bent idempotent functions","authors":"Xiaoyan Chen, Sihong Su","doi":"10.3934/amc.2023022","DOIUrl":"https://doi.org/10.3934/amc.2023022","url":null,"abstract":"","PeriodicalId":50859,"journal":{"name":"Advances in Mathematics of Communications","volume":"44 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77950218","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
The number of codes over rings of order $ 4 $ containing a hull of given type 包含给定类型外壳的$ 4 $阶环上的代码数
IF 0.9 4区 计算机科学
Advances in Mathematics of Communications Pub Date : 2023-01-01 DOI: 10.3934/amc.2023031
Steven T. Dougherty, Esengül Saltürk
{"title":"The number of codes over rings of order $ 4 $ containing a hull of given type","authors":"Steven T. Dougherty, Esengül Saltürk","doi":"10.3934/amc.2023031","DOIUrl":"https://doi.org/10.3934/amc.2023031","url":null,"abstract":"","PeriodicalId":50859,"journal":{"name":"Advances in Mathematics of Communications","volume":"41 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89790397","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
Some subfield codes from MDS codes MDS代码中的一些子字段代码
IF 0.9 4区 计算机科学
Advances in Mathematics of Communications Pub Date : 2023-01-01 DOI: 10.3934/amc.2021023
Can Xiang, Jinquan Luo
{"title":"Some subfield codes from MDS codes","authors":"Can Xiang, Jinquan Luo","doi":"10.3934/amc.2021023","DOIUrl":"https://doi.org/10.3934/amc.2021023","url":null,"abstract":"Subfield codes of linear codes over finite fields have recently received a lot of attention, as some of these codes are optimal and have applications in secrete sharing, authentication codes and association schemes. In this paper, a class of binary subfield codes is constructed from a special family of MDS codes, and their parameters are explicitly determined. The parameters of their dual codes are also studied. Some of the codes presented in this paper are optimal or almost optimal.","PeriodicalId":50859,"journal":{"name":"Advances in Mathematics of Communications","volume":"34 1","pages":"815-827"},"PeriodicalIF":0.9,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87980481","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
A few more optimal optical orthogonal codes with non-constant auto-correlation function 几种具有非常数自相关功能的最优光学正交码
IF 0.9 4区 计算机科学
Advances in Mathematics of Communications Pub Date : 2023-01-01 DOI: 10.3934/amc.2023029
Hengming Zhao, Rongcun Qin, M. Buratti, Dianhua Wu
{"title":"A few more optimal optical orthogonal codes with non-constant auto-correlation function","authors":"Hengming Zhao, Rongcun Qin, M. Buratti, Dianhua Wu","doi":"10.3934/amc.2023029","DOIUrl":"https://doi.org/10.3934/amc.2023029","url":null,"abstract":"","PeriodicalId":50859,"journal":{"name":"Advances in Mathematics of Communications","volume":"77 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88100525","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
New bounds for covering codes of radius 3 and codimension $ 3t+1 $ 覆盖半径为3且余维为3t+1的码的新边界
4区 计算机科学
Advances in Mathematics of Communications Pub Date : 2023-01-01 DOI: 10.3934/amc.2023042
Alexander A. Davydov, Stefano Marcugini, Fernanda Pambianco
{"title":"New bounds for covering codes of radius 3 and codimension $ 3t+1 $","authors":"Alexander A. Davydov, Stefano Marcugini, Fernanda Pambianco","doi":"10.3934/amc.2023042","DOIUrl":"https://doi.org/10.3934/amc.2023042","url":null,"abstract":"","PeriodicalId":50859,"journal":{"name":"Advances in Mathematics of Communications","volume":"12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134979717","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Several formulas for Bernoulli numbers and polynomials 伯努利数和多项式的几个公式
IF 0.9 4区 计算机科学
Advances in Mathematics of Communications Pub Date : 2023-01-01 DOI: 10.3934/AMC.2021006
T. Komatsu, Bijan Kumar Patel, C. Pita-Ruiz
{"title":"Several formulas for Bernoulli numbers and polynomials","authors":"T. Komatsu, Bijan Kumar Patel, C. Pita-Ruiz","doi":"10.3934/AMC.2021006","DOIUrl":"https://doi.org/10.3934/AMC.2021006","url":null,"abstract":"A generalized Stirling numbers of the second kind begin{document}$ S_{a,b}left(p,kright) $end{document} , involved in the expansion begin{document}$ left(an+bright)^{p} = sum_{k = 0}^{p}k!S_{a,b}left(p,kright) binom{n}{k} $end{document} , where begin{document}$ a neq 0, b $end{document} are complex numbers, have studied in [ 16 ]. In this paper, we show that Bernoulli polynomials begin{document}$ B_{p}(x) $end{document} can be written in terms of the numbers begin{document}$ S_{1,x}left(p,kright) $end{document} , and then use the known results for begin{document}$ S_{1,x}left(p,kright) $end{document} to obtain several new explicit formulas, recurrences and generalized recurrences for Bernoulli numbers and polynomials.","PeriodicalId":50859,"journal":{"name":"Advances in Mathematics of Communications","volume":"40 1","pages":"522-535"},"PeriodicalIF":0.9,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76577929","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
Constructions of asymptotically optimal codebooks with respect to Welch bound and Levenshtein bound 关于Welch界和Levenshtein界的渐近最优码本构造
IF 0.9 4区 计算机科学
Advances in Mathematics of Communications Pub Date : 2023-01-01 DOI: 10.3934/amc.2021065
Gang Wang, Deng-Ming Xu, Fang-Wei Fu
{"title":"Constructions of asymptotically optimal codebooks with respect to Welch bound and Levenshtein bound","authors":"Gang Wang, Deng-Ming Xu, Fang-Wei Fu","doi":"10.3934/amc.2021065","DOIUrl":"https://doi.org/10.3934/amc.2021065","url":null,"abstract":"Codebooks with small maximum cross-correlation amplitudes are used to distinguish the signals from different users in code division multiple access communication systems. In this paper, several classes of codebooks are introduced, whose maximum cross-correlation amplitudes asymptotically achieve the corresponding Welch bound and Levenshtein bound. Specially, a class of optimal codebooks with respect to the Levenshtein bound is obtained. These classes of codebooks are constructed by selecting certain rows deterministically from circulant matrices, Fourier matrices and Hadamard matrices, respectively. The construction methods and parameters of some codebooks provided in this paper are new.","PeriodicalId":50859,"journal":{"name":"Advances in Mathematics of Communications","volume":"114 1","pages":"1526-1541"},"PeriodicalIF":0.9,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77721800","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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