Cayley sum graphs and their applications to codebooks

被引：0

作者：

Satake, Shohei ^{[1
]}

Gu, Yujie ^{[2
]}

机构：

[1] Meiji Univ, Sch Interdisciplinary Math Sci, Tokyo 1648525, Japan

[2] Kyushu Univ, Fac Informat Sci & Elect Engn, Fukuoka 8190395, Japan

来源：

DESIGNS CODES AND CRYPTOGRAPHY | 2022年 / 91卷 / 4期

基金：

日本科学技术振兴机构; 日本学术振兴会;

关键词：

Cayley sum graph; Eigenvalue; Gaussian sum; codebook; Welch bound; ASYMPTOTICALLY OPTIMAL CODEBOOKS; COMPRESSED SENSING MATRICES; COMPLEX CODEBOOKS; DETERMINISTIC CONSTRUCTION; BOUNDS;

D O I：

10.1007/s10623-022-01152-x

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

In this paper we first provide two new constructions for Cayley sum graphs, namely, norm-coset graphs and trace-coset graphs, and determine their second largest eigenvalues using Gaussian sums. Next, a connection between Cayley sum graphs and complex codebooks is established. Based on this, infinite families of asymptotically optimal complex codebooks are explicitly constructed. The derived Cayley sum graphs and codebooks either include some known constructions as special cases or provide flexible new parameters.

引用

页码：1315 / 1333

页数：19

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