Optimum Codes Correcting Lattice Errors

In binary transmission through a system of parallel channels, a message can be viewed as a (0,1)-matrix of size $N\times n$, where $N$ is the number of channels and $n$ is the transmission length. We describe a construction of optimal codes which correct any error located in m rows and $s$ columns (lattice errors) provided that $m+s\leq t$, where $t$ is the error-correcting capability of the code.