On synchronizable and PSK-synchronizable block codes

A (finite) code is called synchronizable of th order if, and only if, there exists a least positive integer such that the knowledge of the last letters of any message suffices to determine a separation of code words. This condition is less constraining than the comma-free restriction. Sections I-IV is a description of a way of selecting a synchronizable block code for a given alphabet with letters and a given code-word length n. It is proved that is maximal in the sense that it contains as many words as possible; and an expression is given for the number of words in . Sections V-VIII is a description of a construction of phase-shift-keying synchronizable codes. In the PSK case the letters themselves cannot be identified by the receiver. Only the differences between successive letters can be detected. Thus, if the sequence is transmitted, then the observed sequence in the receiver is . The letters are assumed to be the integers mod ; and is taken mod . This situation occurs in the reading of phase-modulated signals. The construction of these codes (called ) is based on .