Hamming spaces and locally matrix algebras.

We study an abstract class of Hamming spaces (known also as measure algebras) that generalizes standard Hamming spaces (ℤ / 2 ℤ) n . We classify countable locally standard Hamming spaces and show that each of them can be realized as the Boolean algebra of idempotents of a Cartan subalgebra of a locally matrix algebra. [ABSTRACT FROM AUTHOR]