The Maximum Length of Circuit Codes With Long Bit Runs and a New Characterization Theorem

Abstract

We study circuit codes with long bit runs (sequences of distinct transitions) and derive a formula for the maximum length for an infinite class of symmetric circuit codes with long bit runs. This formula also results in an improved lower bound on the maximum length for an infinite class of circuit codes without restrictions on symmetry or bit run length. We also present a new characterization of circuit codes of spread $k$ based on a theorem of Deimer.