A Family of Comma-Free Codes with Even Word-Length

Abstract

For even codeword length $n=2k,k>1$ and alphabet size $\sigma >1$, a family of comma-free codes is constructed with

$${\lfloor \frac{{\sigma }^2}{3}\rfloor }^r{({\sigma }^2–\lfloor \frac{{\sigma }^2}{3}\rfloor )}^{k-r}$$

codewords where $1\le r<k$. In particular, a new maximal comma-free code with $n=4$ and $\sigma =4$ is given by one of these codes.