The Meet Operation in the Imbalance Lattice of Maximal Instantaneous Codes: Alternative Proof of Existence

Abstract

An alternative proof is given of the existence of greatest lower bounds in the imbalance order of binary maximal instantaneous codes of a given size. These codes are viewed as maximal antichains of a given size in the infinite binary tree of 0–1 words. The proof proposed makes use of a single balancing operation within the same imbalance poset of codes of the same fixed size, instead of moving back and forth between posets of codes corresponding to two different code sizes using expansion and contraction, as in the previous proofs of the existence of glb. It also makes use of a new combinatorial characterization of the imbalance order.