Construction of cyclotomic codebooks nearly meeting the Welch bound

摘要

Ding and Feng (IEEE Trans Inform Theory 52(9):4229-235,2006, IEEE Trans Inform Theory 53(11):4245-4250,2007) constructed series of (N, K) codebooks which meet or nearly meet the Welch bound N-K/(N-1)~K~(1/2) by using difference set (DS) or almost difference set (ADS) in certain finite abelian group respectively. In this paper, we generalize the cyclotomic constructions considered in (IEEE Trans Inform Theory 52(9):4229-4235,2006, IEEE Trans Inform Theory 53(11):4245-4250,2007) and (IEEE Trans Inform Theory 52(5), 2052-2061,2006) to present more series of codebooks which nearly meet the Welch bound under looser conditions than ones required by DS and ADS.