Complex Golay pairs up to length 28: A search via computer algebra and programmatic SAT
نویسندگان
چکیده
منابع مشابه
A computer search for complex Golay sequences
We report on a computer search for complex Golay sequences of short length. All such sequences of length 11 and 13 will be classified.
متن کاملQuaternary Golay sequence pairs I: even length
The origin of all 4-phase Golay sequences and Golay sequence pairs of even length at most 26 is explained. The principal techniques are the three-stage construction of Fiedler, Jedwab and Parker [FJP08] involving multi-dimensional Golay arrays, and a “sum-difference” construction that modifies a result due to Eliahou, Kervaire and Saffari [EKS91]. The existence of 4-phase seed pairs of lengths ...
متن کاملQuaternary Golay sequence pairs II: odd length
A 4-phase Golay sequence pair of length s ≡ 5 (mod 8) is constructed from a Barker sequence of the same length whose even-indexed elements are prescribed. This explains the origin of the 4-phase Golay seed pairs of length 5 and 13. The construction cannot produce new 4-phase Golay sequence pairs, because there are no Barker sequences of odd length greater than 13. A partial converse to the cons...
متن کاملMATHCHECK: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers
We present a method and an associated system, called MATHCHECK, that embeds the functionality of a computer algebra system (CAS) within the inner loop of a conflict-driven clause-learning SAT solver. SAT+CAS systems, a la MATHCHECK, can be used as an assistant by mathematicians to either counterexample or finitely verify open universal conjectures on any mathematical topic (e.g., graph and numb...
متن کاملGolay complementary array pairs
Constructions and nonexistence conditions for multi-dimensional Golay complementary array pairs are reviewed. A construction for a d-dimensional Golay array pair from a (d+1)-dimensional Golay array pair is given. This is used to explain and expand previously known constructive and nonexistence results in the binary case.
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ژورنال
عنوان ژورنال: Journal of Symbolic Computation
سال: 2021
ISSN: 0747-7171
DOI: 10.1016/j.jsc.2019.10.013