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Abstract. A domain R is said to have the finite factorization property if every nonzero non-unit element of R has at least one and at most finitely many distinct factorizations up to multiplication of irreducible factors by central units. Let k be an algebraically closed field and let A be a k-algebra. We show that if A has an associated graded ring that is a domain with the property that the dimension of each homogeneous component is finite then A is a finite factorization domain. As a corollary, we show that many classes of algebras have the finite factorization property, including Weyl algebras, enveloping algebras of finite-dimensional Lie algebras, quantum affine spaces and shift algebras. This provides a termination criterion for factorization procedures over these algebras. In addition, we give explicit upper bounds on the number of distinct factorizations of an element in terms of data from the filtration.

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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 [11] that confirms the 2002 conjecture of Craigen, Holzmann, and Kharaghani [8] 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.