Cayley sum graphs and their applications to codebooks

Shohei Satake; Yujie Gu

doi:10.1007/s10623-022-01152-x

Cayley sum graphs and their applications to codebooks

Shohei Satake, Yujie Gu

Mathematical Informatics

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	English
Pages (from-to)	1315-1333
Number of pages	19
Journal	Designs, Codes, and Cryptography
Volume	91
Issue number	4
DOIs	https://doi.org/10.1007/s10623-022-01152-x
Publication status	Published - Apr 2023

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Computer Science Applications
Discrete Mathematics and Combinatorics
Applied Mathematics

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abstract = "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.",

author = "Shohei Satake and Yujie Gu",

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Cayley sum graphs and their applications to codebooks

Abstract

All Science Journal Classification (ASJC) codes

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