Computing Binary Combinatorial Gray Codes Via Exhaustive Search With SAT Solvers

Abstract

The term binary combinatorial Gray code refers to a list of binary words such that the Hamming distance between two neighboring words is one and the list satisfies some additional properties that are of interest to a particular application, e.g., circuit testing, data compression, and computational biology. New distance-preserving and circuit codes are presented along with a complete list of equivalence classes of the coil-in-the-box codes for codeword length with respect to symmetry transformations of hypercubes. A Gray-ordered code composed of all necklaces of the length is presented, improving the known result with length .