Inductive Constructions of Perfect Ternary Constant-Weight Codes with Distance 3

We propose inductive constructions of perfect (n,3;n – 1)3 codes (ternary constant-weight codes of length n and weight n – 1 with distance 3), which are modifications of constructions of perfect binary codes. The construction yields at least \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$2^{2^{n/2 - 2} }$$ \end{document} different perfect (n,3;n – 1)3 codes. To perfect (n,3;n – 1)3 codes, perfect matchings in a binary hypercube without close (at distance 1 or 2 from each other) parallel edges are equivalent.