2021
DOI: 10.1016/j.jsc.2019.10.013
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Complex Golay pairs up to length 28: A search via computer algebra and programmatic SAT

Abstract: We use techniques from the fields of computer algebra and satisfiability checking to develop a new algorithm to search for complex Golay pairs. We implement this algorithm and use it to perform a complete search for complex Golay pairs of lengths up to 28. In doing so, we find that complex Golay pairs exist in the lengths 24 and 26 but do not exist in the lengths 23, 25, 27, and 28. This independently verifies work done by F. Fiedler in 2013 and confirms the 2002 conjecture of Craigen, Holzmann, and Kharaghani… Show more

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Cited by 8 publications
(5 citation statements)
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“…Programmatic SAT solvers were introduced by Ganesh et al [11] in order to solve an RNA folding problem. They have since been used to search for various combinatorial objects such as Williamson matrices [5], best matrices [7], and complex Golay sequences [6].…”
Section: Symbolic Computation and Sat+casmentioning
confidence: 99%
“…Programmatic SAT solvers were introduced by Ganesh et al [11] in order to solve an RNA folding problem. They have since been used to search for various combinatorial objects such as Williamson matrices [5], best matrices [7], and complex Golay sequences [6].…”
Section: Symbolic Computation and Sat+casmentioning
confidence: 99%
“…However, this result had never been independently verified. Using MathCheck we performed the first independent verification of this result [15] by explicitly finding all complex Golay pairs for n ≤ 28, and further provided a complete enumeration of all inequivalent complex Golay pairs up to 28.…”
Section: The Sat+cas Paradigmmentioning
confidence: 99%
“…Additionally, the entries of best matrices can be shown to satisfy certain constraints similar to constraints that Williamson matrices [74], good matrices [9], and the coefficients of complex Golay pairs [15] satisfy. In the appendix we show that the entries of best matrices satisfy the relationship a k b k c k d k a 2k b 2k c 2k = −1 for k = 0 with indices reduced mod n. Because of the anti-symmetry of A, B, and C, when k = n/3 the product constraint reduces to d k = 1 and in this case can be encoded as a unit clause.…”
Section: Conquer Phasementioning
confidence: 99%
See 1 more Smart Citation
“…MathCheck can be used to independently verify the results of Fiedler's searches [8,9]. e rst step is to nd all single polynomials f that could appear as a member of a complex Golay pair.…”
Section: Craigen-holzmann-kharaghani Conjecturementioning
confidence: 99%