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

A kk-ary charm bracelet is an equivalence class of length nn strings with the action on the indices by the additive group of the ring of integers modulo nn extended by the group of units. By applying an O(n3)O(n3) amortized time algorithm to generate charm bracelet representatives with a specified content, we construct 29 new periodic Golay pairs of length 68.