Abstract
Let p, q be distinct primes with gcd(p − 1, q − 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.
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Communicated by K. T. Arasu.
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Hu, L., Yue, Q. Gauss periods and codebooks from generalized cyclotomic sets of order four. Des. Codes Cryptogr. 69, 233–246 (2013). https://doi.org/10.1007/s10623-012-9648-8
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DOI: https://doi.org/10.1007/s10623-012-9648-8