Multiply constant weight codes

The function M(m, n, d, w), the largest size of an unrestricted binary code made of m by n arrays, with constant row weight w, and minimum distance d is introduced and compared to the classical functions of combinatorial coding theory A_q(n, d) and A(n, d, w). The analogues for systematic codes of A(n, d) and A(n, d, w) are introduced apparently for the first time. An application to the security of embedded systems is given: these codes happen to be efficient challenges for physically unclonable functions.