On the Generation of Aperiodic and Periodic Necklaces via T-augmentation
Thomas Aaron Gulliver, Isaiah Makwakwa, Ulrich Speidel · ResearchSpace (University of Auckland) · 2008
In a recent report, Gulliver and Speidel showed that complete sets of aperiodic and – in some cases periodic – necklaces can be generated for arbitrary lengths as fixed-length subsets of variable-length T-codes. The T-codes to which they applied this observation were specifically Tcodes constructed by systematic T-augmentation, that is by T-augmentation sequences in which each T-expansion parameter is 1 (simple T-augmentation) and where the T-codes A(p1,p2,...,pi) at each Taugmentation level i do not contain any codewords shorter than pi (strictly minimal T-augmentation). This present paper generalizes their result to arbitrary T-codes and formalizes their earlier result as a special case of the general result.