Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra, 3/e (Undergraduate Texts in Mathematics)
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New families of unimodular sequences of length p = 3f + 1 with zero autocorrelation are described, p being a prime. The construction is based on employing Gauss periods. It is shown that in this case elements of the sequences are algebraic numbers defined by irreducible polynomials over \mathbb{Z} of degree 12 (for the first family) and 6 (for the second family). In turn, these polynomials are factorized in some extension of the field \mathbb{Q} into polynomials of degree, respectively, 4 and 2, which are written explicitly. For p = 13, using the exhaustive search method, full classification of unimodular sequences with zero autocorrelation is given.