Symmetry Implies Isomorphism for Certain Maximum Length Circuit Codes

Abstract

A classic result due to Douglas [2] establishes that, for odd spread k and dimension d = 1 2 (3k + 3), all maximum length (d, k) circuit codes are isomorphic. Using a recent result of Byrnes [1] we extend Douglas's theorem to prove that, for k even ≥ 4 and d = 1 2 (3k + 4), all maximum length symmetric (d, k) circuit codes are isomorphic.