Two constructions of asymptotically optimal codebooks via the trace functions
Information Theory
2019-05-07 v1 math.IT
Abstract
In this paper, we present two new constructions of complex codebooks with multiplicative characters, additive characters and trace functions over finite fields, and determine the maximal cross-correlation amplitude of these codebooks. We prove that the codebooks we constructed are asymptotically optimal with respect to the Welch bound. Moreover, in the first construction, we generalize the result in [28]. In the second construction, we generalize the results in [12], we can achieve Welch bound for any odd prime p, we also derive the whole distribution of their inner products. The parameters of these codebooks are new.
Keywords
Cite
@article{arxiv.1905.01815,
title = {Two constructions of asymptotically optimal codebooks via the trace functions},
author = {Xia Wu and Wei Lu and Xiwang Cao and Ming Chen},
journal= {arXiv preprint arXiv:1905.01815},
year = {2019}
}
Comments
15 pages, 3tables