TY - JOUR
T1 - Cayley sum graphs and their applications to codebooks
AU - Satake, Shohei
AU - Gu, Yujie
N1 - Funding Information:
The authors are very grateful to the anonymous reviewers and associated editor for their insightful and constructive comments and suggestions. The authors would like to thank Professor Ofer Shayevitz and Professor Rami Zamir for helpful discussions. S. Satake has been supported by Grant-in-Aid for JSPS Fellows 18J11282 and 20J00469 of the Japan Society for the Promotion of Science and ACT-X JPMJAX2109 of the Japan Science and Technology Agency. Y. Gu has been supported by Grant-in-Aid for Early-Career Scientists 21K13830 of the Japan Society for the Promotion of Science. Parts of this work were presented at [].
Publisher Copyright:
© 2022, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.
PY - 2022
Y1 - 2022
N2 - 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.
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.
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U2 - 10.1007/s10623-022-01152-x
DO - 10.1007/s10623-022-01152-x
M3 - Article
AN - SCOPUS:85142217595
SN - 0925-1022
JO - Designs, Codes, and Cryptography
JF - Designs, Codes, and Cryptography
ER -