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On base and Turyn sequences


Authors: C. Koukouvinos, S. Kounias and K. Sotirakoglou
Journal: Math. Comp. 55 (1990), 825-837
MSC: Primary 62K10
DOI: https://doi.org/10.1090/S0025-5718-1990-1023764-7
MathSciNet review: 1023764
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Abstract: Base sequences of lengths $ n + 1$, $ n + 1$, n, n are constructed for all decompositions of $ 4n + 2$ into four squares for $ n = 19, \ldots ,24$. The construction is achieved through an algorithm which is also presented. It is proved through an exhaustive search that Turyn sequences do not exist for $ n = 18, \ldots ,27$; since Turyn sequences cannot exist for $ n = 28$ or 29, the first unsettled case is $ n = 30$.


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DOI: https://doi.org/10.1090/S0025-5718-1990-1023764-7
Keywords: Associate polynomial, algorithm, autocorrelation, cross-correlation, construction
Article copyright: © Copyright 1990 American Mathematical Society