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^*

^*Corresponding author for this work

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
State	Published - Apr 2023
Externally published	Yes

Keywords

Cayley sum graph
Eigenvalue
Gaussian sum
Welch bound
codebook

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10.1007/s10623-022-01152-x

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keywords = "Cayley sum graph, Eigenvalue, Gaussian sum, Welch bound, codebook",

author = "Shohei Satake and Yujie Gu",

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AB - 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.

KW - Cayley sum graph

KW - Eigenvalue

KW - Gaussian sum

KW - Welch bound

KW - codebook

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Cayley sum graphs and their applications to codebooks

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Keywords

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