Charm bracelets and their application to the construction of periodic Golay pairs

Abstract

A $k$-ary charm bracelet is an equivalence class of length $n$ strings with the action on the indices by the additive group of the ring of integers modulo $n$ extended by the group of units. By applying an $O(n^3)$ amortized time algorithm to generate charm bracelet representatives with a specified content, we construct 29 new periodic Golay pairs of length $68$.

15 pages, revised and updated version

References in corpus (3)

• Compression of Periodic Complementary Sequences and Applications
• Some new periodic Golay pairs
• Periodic Golay pairs of length 72

Cited by in corpus (2)

• Some new periodic Golay pairs
• There is no circulant weighing matrix of order 60 and weight 36