Synchronization of Isolated Words of MDS Codes in Noise

The article considers synchronization of code words $(n,k)$ of maximum-distance separable codes (MDS codes) in the case of which each code arrives from the channel in noise. The author introduces the concept of the index of nonintersection at ${n-s}$ positions $(m_{n-s})$ as the minimum of the paired distances between ${n-s}$ symbol prefixes and ${n-s}$ symbol suffixes of code words under shift $s$. A method of constructing MDS codes with maximum $m_{n-s}$ values is given, as well as relations that make it possible to determine $P_{\rm{sun}}(s)$ (the probability of false synchronization) for them and to estimate $P_e(s)$ (the probability of error associated with false synchronization). Results of numerical computer calculations are presented.