A Construction of Codebooks Nearly Achieving the Levenstein Bound

Abstract

Codebooks with small inner-product correlation are preferred in many practical applications such as direct spread code division multiple access communications, coding theory, and compressed sensing. The well-known Welch bound and Levenstein bound are useful benchmarks for the correlation of codebooks. In general, it is very hard to obtain codebooks achieving the Welch bound or the Levenstein bound. The objective of this letter is to present a construction of codebooks based on additive and multiplicative characters of finite fields. It generates codebooks nearly achieving the Levenstein bound.