Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Complex Golay Pairs up to Length 28: A Search via Computer Algebra and
  Programmatic SAT   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 that complex Golay
pairs of length 23 don't exist. Our algorithm is based on the recently proposed
SAT+CAS paradigm of combining SAT solvers with computer algebra systems to
efficiently search large spaces specified by both algebraic and logical
constraints. The algorithm has two stages: first, a fine-tuned computer program
uses functionality from computer algebra systems and numerical libraries to
construct a list containing every sequence which could appear as the first
sequence in a complex Golay pair up to equivalence. Second, a programmatic SAT
solver constructs every sequence (if any) that pair off with the sequences
constructed in the first stage to form a complex Golay pair. This extends work
originally presented at the International Symposium on Symbolic and Algebraic
Computation (ISSAC) in 2018; we discuss and implement several improvements to
our algorithm that enabled us to improve the efficiency of the search and
increase the maximum length we search from length 25 to 28.

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The categories of this paper are: comp-gas
10
The categories of this paper are: q-bio
24
The categories of this paper are: dg-ga
9
The categories of this paper are: nlin
36
The categories of this paper are: cmp-lg
8
The categories of this paper are: hep-ex
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The categories of this paper are: patt-sol
14
The categories of this paper are: math-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: q-fin
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The categories of this paper are: plasm-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: stat
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The categories of this paper are: solv-int
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The categories of this paper are: quant-ph
7
The categories of this paper are: hep-th