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Applied Algebra and Number Theory最新文献

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Controlling the shape of generating matrices in global function field constructions of digital sequences 数字序列全局函数域构造中生成矩阵的形状控制
Applied Algebra and Number Theory Pub Date : 1900-01-01 DOI: 10.1017/CBO9781139696456.011
Roswitha Hofer, Isabel Pirsic
{"title":"Controlling the shape of generating matrices in global function field constructions of digital sequences","authors":"Roswitha Hofer, Isabel Pirsic","doi":"10.1017/CBO9781139696456.011","DOIUrl":"https://doi.org/10.1017/CBO9781139696456.011","url":null,"abstract":"Motivated by computational as well as theoretical considerations we show how the shape and density of the generating matrices of two optimal constructions of (t, s)and (u, e, s)-sequences (viz., the Xing-Niederreiter and Hofer-Niederreiter sequences) can be controlled by a careful choice of various parameters. We also present some experimental data to support our assertions and point out open problems. MSC2010: 11K31, 11K38.","PeriodicalId":352591,"journal":{"name":"Applied Algebra and Number Theory","volume":"85 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114563963","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
On the linear complexity of multisequences, bijections between ℤahlen and ℕumber tuples, and partitions 关于多序列的线性复杂度，以及若干元组与若干元组之间的对射和划分
Applied Algebra and Number Theory Pub Date : 1900-01-01 DOI: 10.1017/CBO9781139696456.019
M. Vielhaber
{"title":"On the linear complexity of multisequences, bijections between ℤahlen and ℕumber tuples, and partitions","authors":"M. Vielhaber","doi":"10.1017/CBO9781139696456.019","DOIUrl":"https://doi.org/10.1017/CBO9781139696456.019","url":null,"abstract":"","PeriodicalId":352591,"journal":{"name":"Applied Algebra and Number Theory","volume":"35 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127113031","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Index bounds for value sets of polynomials over finite fields 有限域上多项式值集的索引界
Applied Algebra and Number Theory Pub Date : 1900-01-01 DOI: 10.1017/CBO9781139696456.017
G. Mullen, D. Wan, Qiang Wang
{"title":"Index bounds for value sets of polynomials over finite fields","authors":"G. Mullen, D. Wan, Qiang Wang","doi":"10.1017/CBO9781139696456.017","DOIUrl":"https://doi.org/10.1017/CBO9781139696456.017","url":null,"abstract":"We provide an upper bound for the cardinality of the value set of a univariate polynomial over a finite field in terms of the index of the polynomial. Moreover, we study when a polynomial vector map in n variables is a permutation polynomial map, again using the index tuple of the map. This also provides an upper bound for the value set of a polynomial map in n variables.","PeriodicalId":352591,"journal":{"name":"Applied Algebra and Number Theory","volume":"12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131334431","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 7
Asymptotic formulas for partitions with bounded multiplicity 有界多重分区的渐近公式
Applied Algebra and Number Theory Pub Date : 1900-01-01 DOI: 10.1017/CBO9781139696456.015
P. Liardet, Alain Thomas
{"title":"Asymptotic formulas for partitions with bounded multiplicity","authors":"P. Liardet, Alain Thomas","doi":"10.1017/CBO9781139696456.015","DOIUrl":"https://doi.org/10.1017/CBO9781139696456.015","url":null,"abstract":"","PeriodicalId":352591,"journal":{"name":"Applied Algebra and Number Theory","volume":"134 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125756073","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
On an important family of inequalities of Niederreiter involving exponential sums 关于涉及指数和的一类重要的尼德雷特不等式
Applied Algebra and Number Theory Pub Date : 1900-01-01 DOI: 10.1017/CBO9781139696456.010
P. Hellekalek
{"title":"On an important family of inequalities of Niederreiter involving exponential sums","authors":"P. Hellekalek","doi":"10.1017/CBO9781139696456.010","DOIUrl":"https://doi.org/10.1017/CBO9781139696456.010","url":null,"abstract":"The inequality of Erdos-Turan-Koksma is a fundamental tool to bound the discrepancy of a sequence in the s-dimensional unit cube [0, 1), s ≥ 1, in terms of exponential sums. In an impressive series of papers, Harald Niederreiter has established variants of this inequality and has proved bounds for the discrepancy for various sequences and point sets, in the context of pseudo-random number generation and in quasi-Monte Carlo methods. These results have been an important breakthrough, because they marked the starting point of a thorough theoretical correlation analysis of pseudo-random numbers. Niederreiter’s technique also prepared for the study of digital sequences, which are central to modern quasi-Monte Carlo methods. In this contribution, we present an overview of these concepts and prove a hybrid version of the inequality of Erdos-Turan-Koksma, thereby extending a recent result of Niederreiter.","PeriodicalId":352591,"journal":{"name":"Applied Algebra and Number Theory","volume":"693 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131954849","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Rational points of the curve over 曲线上的有理点
Applied Algebra and Number Theory Pub Date : 1900-01-01 DOI: 10.1017/CBO9781139696456.018
F. Özbudak, Zülfükar Saygı
{"title":"Rational points of the curve over","authors":"F. Özbudak, Zülfükar Saygı","doi":"10.1017/CBO9781139696456.018","DOIUrl":"https://doi.org/10.1017/CBO9781139696456.018","url":null,"abstract":"","PeriodicalId":352591,"journal":{"name":"Applied Algebra and Number Theory","volume":"34 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123574738","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A trigonometric approach for Chebyshev polynomials over finite fields 有限域上切比雪夫多项式的三角方法
Applied Algebra and Number Theory Pub Date : 1900-01-01 DOI: 10.1017/CBO9781139696456.016
Juliano B. Lima, D. Panario, R. Souza
{"title":"A trigonometric approach for Chebyshev polynomials over finite fields","authors":"Juliano B. Lima, D. Panario, R. Souza","doi":"10.1017/CBO9781139696456.016","DOIUrl":"https://doi.org/10.1017/CBO9781139696456.016","url":null,"abstract":"In this paper, we introduce trigonometric definitions for Chebyshev polynomials over finite fields Fq , where q = pm , m is a positive integer and p is an odd prime. From such definitions, we derive recurrence relations which are equivalent to those established for real valued Chebyshev polynomials and for Chebyshev polynomials of the first and second kinds over finite fields. Periodicity and symmetry properties of these polynomials are also studied. Such properties are then used to derive sufficient conditions for the Chebyshev polynomials of the second, third and fourth kinds over finite fields to be permutation polynomials.","PeriodicalId":352591,"journal":{"name":"Applied Algebra and Number Theory","volume":"33 5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116750599","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 8
A heuristic formula estimating the keystream length for the general combination generator with respect to a correlation attack 针对相关攻击，给出了一种估计通用组合发生器密钥流长度的启发式公式
Applied Algebra and Number Theory Pub Date : 1900-01-01 DOI: 10.1017/CBO9781139696456.007
R. Göttfert
{"title":"A heuristic formula estimating the keystream length for the general combination generator with respect to a correlation attack","authors":"R. Göttfert","doi":"10.1017/CBO9781139696456.007","DOIUrl":"https://doi.org/10.1017/CBO9781139696456.007","url":null,"abstract":"","PeriodicalId":352591,"journal":{"name":"Applied Algebra and Number Theory","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128437017","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","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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