Pub Date : 2018-09-10DOI: 10.1109/IWSDA46143.2019.8966118
Sihem Mesnager, Ahmet Sınak
This paper presents the first construction of strongly regular graphs and association schemes from weakly regular plateaued functions over the finite fields of odd characteristic. Indeed, we generalize the construction method of strongly regular graphs from weakly regular bent functions given by Chee et al. [Journal of Algebraic Combinatorics, 34(2), 251–266, 2011] to weakly regular plateaued functions. In this framework, we construct strongly regular graphs with three types of parameters from weakly regular plateaued functions with some homogeneous conditions. We also construct a family of association schemes of class p from weakly regular plateaued p-ary functions.
本文给出了奇特征有限域上弱正则平台函数的强正则图的第一个构造和关联方案。实际上，我们将Chee et al.[代数组合学报，34(2)，251-266,2011]给出的弱正则弯曲函数的强正则图的构造方法推广到弱正则平台函数。在这个框架中，我们从具有齐次条件的弱正则平台函数构造了具有三种参数的强正则图。我们还从弱正则平台p- y函数构造了一类p类的关联格式。
{"title":"Strongly Regular Graphs from Weakly Regular Plateaued Functions*","authors":"Sihem Mesnager, Ahmet Sınak","doi":"10.1109/IWSDA46143.2019.8966118","DOIUrl":"https://doi.org/10.1109/IWSDA46143.2019.8966118","url":null,"abstract":"This paper presents the first construction of strongly regular graphs and association schemes from weakly regular plateaued functions over the finite fields of odd characteristic. Indeed, we generalize the construction method of strongly regular graphs from weakly regular bent functions given by Chee et al. [Journal of Algebraic Combinatorics, 34(2), 251–266, 2011] to weakly regular plateaued functions. In this framework, we construct strongly regular graphs with three types of parameters from weakly regular plateaued functions with some homogeneous conditions. We also construct a family of association schemes of class p from weakly regular plateaued p-ary functions.","PeriodicalId":326214,"journal":{"name":"2019 Ninth International Workshop on Signal Design and its Applications in Communications (IWSDA)","volume":"52 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122687337","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}
Pub Date : 2017-11-18DOI: 10.1109/IWSDA46143.2019.8966124
Lei Deng
Denote $mathcal{A}$ as the set of all doubly substochastic m×n matrices and let k be a positive integer. Let $mathcal{A}_k$ be the set of all 1/k-bounded doubly substochastic m × n matrices, i.e., $mathcal{A}_k triangleq {E in mathcal{A}:e_{i,j} in [0,1/k],forall i = 1,2, cdots ,m,j = 1,2, cdots ,n}$. Denote ℬk as the set of all matrices in $mathcal{A}_k$ whose entries are either 0 or 1/k. We prove that $mathcal{A}_k$ is the convex hull of all matrices in ℬk. In addition, we introduce an application of this result in communication system.
记$mathcal{A}$为所有双次随机m×n矩阵的集合，设k为正整数。设$mathcal{A}_k$是所有1/k有界的双次随机m × n矩阵的集合，即$mathcal{A}_k triangleq {E in mathcal{A}:e_{i,j} in [0,1/k]，forall i = 1,2， cdots,m,j = 1,2， cdots,n}$。记作$mathcal{A}_k$中所有元素为0或1/k的矩阵的集合。证明了$mathcal{A}_k$是所有矩阵的凸包。此外，还介绍了该结果在通信系统中的应用。
{"title":"Convex Set of Doubly Substochastic Matrices","authors":"Lei Deng","doi":"10.1109/IWSDA46143.2019.8966124","DOIUrl":"https://doi.org/10.1109/IWSDA46143.2019.8966124","url":null,"abstract":"Denote $mathcal{A}$ as the set of all doubly substochastic m×n matrices and let k be a positive integer. Let $mathcal{A}_k$ be the set of all 1/k-bounded doubly substochastic m × n matrices, i.e., $mathcal{A}_k triangleq {E in mathcal{A}:e_{i,j} in [0,1/k],forall i = 1,2, cdots ,m,j = 1,2, cdots ,n}$. Denote ℬk as the set of all matrices in $mathcal{A}_k$ whose entries are either 0 or 1/k. We prove that $mathcal{A}_k$ is the convex hull of all matrices in ℬk. In addition, we introduce an application of this result in communication system.","PeriodicalId":326214,"journal":{"name":"2019 Ninth International Workshop on Signal Design and its Applications in Communications (IWSDA)","volume":"63 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-11-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121917287","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}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：