Coset decomposition in lattices yields sample-block number systems

The representation of a scalar by a sequence of digits weighted by powers of some radix is here generalized to vectors. The radix becomes a matrix, and its powers are applied to digits that are vectors taken from a lattice. Familiar notions of overflow and truncation error apply, and the familiar two\´s-complement approach to representing vectors on the "wrong side" of zero generalizes cleanly. Blocking 1D samples into vectors before conversion to these vector number systems can yield advantages in computational efficiency related to the packing efficiency of lattice points, much as data communication is improved by error-correcting block codes, a closely related topic