Codebooks from almost difference sets
Designs, Codes and Cryptography
Autocorrelation values of generalized cyclotomic sequences of order two
IEEE Transactions on Information Theory
Lower bounds on the maximum cross correlation of signals (Corresp.)
IEEE Transactions on Information Theory
Achieving the Welch bound with difference sets
IEEE Transactions on Information Theory
Complex Codebooks From Combinatorial Designs
IEEE Transactions on Information Theory
A Generic Construction of Complex Codebooks Meeting the Welch Bound
IEEE Transactions on Information Theory
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Let p, q be distinct primes with gcd(p 驴 1, q 驴 1) = 4. Let D 0, D 1, D 2, D 3 be Whiteman's generalized cyclotomic classes, satisfying the multiplicative group $${{\mathbb Z}^*_{pq}=D_0\cup D_1\cup D_2\cup D_3}$$ . In this paper, we give formulas of Gauss periods: $${\sum_{i\in D_0\cup D_2}\zeta^i}$$ and $${\sum_{i\in D_0}\zeta^i}$$ , where $${\zeta}$$ is a pqth primitive root of unity. As an application, we get the maximum cross-correlation amplitudes of three codebooks from generalized cyclotomic sets of order four and supply conditions on p and q such that they nearly meet the Welch bound.