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

\[
{\left\lfloor \frac{\sigma^2}{3} \right\rfloor}^r \left( \sigma^2 – \left\lfloor \frac{\sigma^2}{3} \right\rfloor \right)^{k-r}
\]

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