Binary templates for comma-free DNA codes

Arita and Kobayashi proposed a method for constructing comma-free DNA codes using binary templates, and showed that the separation d of any such binary template of length n   satisfies d⩽n/2d⩽n/2. Kobayashi, Kondo and Arita later produced an infinite family of binary templates with d⩾11n/30.d⩾11n/30. Here we demonstrate the existence of an infinite family of binary templates with d>n/2-(18nlogen)1/2. We also give an explicit construction for an infinite family of binary templates with d>n/2-19n1/2logen.