Cayley sum graphs and their applications to codebooks

Shohei Satake, Yujie Gu*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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 languageEnglish
Pages (from-to)1315-1333
Number of pages19
JournalDesigns, Codes, and Cryptography
Issue number4
StatePublished - Apr 2023
Externally publishedYes


  • Cayley sum graph
  • Eigenvalue
  • Gaussian sum
  • Welch bound
  • codebook


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