A Family of Circular Systematic Comma-Free Codes

Abstract

Comma-free codes are used to correct synchronization errors in sequential transmission. Systematic comma-free codes have codewords with fixed positions for error correction. We consider only comma-free codes with constant word length $n>1$. Circular codes use the integers mod $n$ as indices for codeword entries. We first show two easily stated conditions are equivalent to the existence question for circular systematic comma-free codes over arbitrary finite alphabets. For $n>3$ a family of circular systematic comma-free codes with word length $n=p$, a prime, is constructed, each corresponding to a fair partition of a difference set in ${\mathbb{Z}}_n$.