Exhaustive Search for Maximal Length Coil-in-the-Box Codes

An n-bit coil is a sequence of length n binary strings which corresponds to an induced cycle in the n-dimension hypercube. Coils have a variety of applications and usually the longer the coil the more useful it is in the application. The longest possible coils for n ≤ 7 were found by exhaustive search. Several heuristic based computational techniques including stochastic hill-climbing technique, genetic algorithms, neural network and other evolutionary algorithms have been used to find a lower bound for the maximum length of coils for n = 8, 9, 10, 11 and 12. Most of the current approaches on this problem were built on the exhaustive search algorithm in [Koc96] which currently requires more than a month of computation time to exhaustively search the longest coils for n = 7. In this paper, we describe some heuristics that can improve the runtime for the exhaustive search of the longest coils. There is an improvement by a factor of approximately 18 on the runtime for an exhaustive search for n = 7 when compared to [Koc96].