Article thumbnail

Enumeration of Complex Golay Pairs via Programmatic SAT

By Curtis Bright, Ilias Kotsireas, Albert Heinle and Vijay Ganesh

Abstract

We provide a complete enumeration of all complex Golay pairs of length up to 25, verifying that complex Golay pairs do not exist in lengths 23 and 25 but do exist in length 24. This independently verifies work done by F. Fiedler in 2013 that confirms the 2002 conjecture of Craigen, Holzmann, and Kharaghani that complex Golay pairs of length 23 don't exist. Our enumeration method relies on the recently proposed SAT+CAS paradigm of combining computer algebra systems with SAT solvers to take advantage of the advances made in the fields of symbolic computation and satisfiability checking. The enumeration proceeds in two stages: First, we use a fine-tuned computer program and functionality from computer algebra systems to construct a list containing all sequences which could appear as the first sequence in a complex Golay pair (up to equivalence). Second, we use a programmatic SAT solver to construct all sequences (if any) that pair off with the sequences constructed in the first stage to form a complex Golay pair.Comment: Corrected typo

Topics: Computer Science - Logic in Computer Science, Computer Science - Symbolic Computation, Mathematics - Combinatorics
Publisher: 'Association for Computing Machinery (ACM)'
Year: 2018
DOI identifier: 10.1145/3208976.3209006
OAI identifier: oai:arXiv.org:1805.05488

Suggested articles


To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.