A Family of Circular Systematic Comma-Free Codes

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 \( \mathbb{Z}_n \).