Abstract
Ding and Feng (IEEE Trans Inform Theory 52(9):4229---4235, 2006, IEEE Trans Inform Theory 53(11):4245---4250, 2007) constructed series of (N, K) codebooks which meet or nearly meet the Welch bound $${\sqrt{\frac{N-K}{(N-1)K}}}$$ 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.
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