Charm bracelets and their application to the construction of periodic   Golay pairs
  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 $68$. 
Dragomir Z Djokovic, Ilias Kotsireas, Daniel Recoskie and Joe Sawada
math.CO