Upper bound on the capacity of constrained three-dimensional codes
An upper bound on the capacity of constrained three-dimensional codes is presented. The bound for two-dimensional codes of Calkin and Wilf (see SIAM Journal of Discrete Mathematics, vol.11, no.1, p.54-60, 1998) was extended to three dimensions by Nagy and Zeger. Both bounds apply to first order symmetric constraints. The bound in three dimensions is generalized in a weaker form to higher order and non-symmetric constraints.