Welcome to the Lattice Kingdom.

Lattice-based code Encodes states (codewords) in coordinates of a lattice in the $$n$$-dimensional real coordinate space $$\mathbb{R}^n$$. The number of codewords may be infinite because the coordinate space is infinite-dimensional, so various restricted versions have to be constructed in practice. Since lattices are closed under addition, lattice-based codes can be thought of as linear codes over the reals. Parents: Error-correcting code (ECC). Cousins: Linear binary code. Cousin of: Group-based code, Multi-mode GKP code.