The Number of the Two Dimensional Run Length Constrained Arrays
Talip Atajan, Naohisa Otsuka, Xuerong Yong · 2011
First, a new framework describing the transfer matrices for the two dimensional run length constrained arrays (codes) is introduced, and some important properties of the transfer matrices (1 ) m Tm are derived in this framework. Then, using these properties, it is shown that the numbers (, ) ( , 1) Nm n m n of the two dimensional binary arrays satisfying the (1, ) - run length constraint is expressible by a linear recurrence equation of a fixed order, approximately equal to dim( ) 2 m T. Finally, to demonstrate the effectiveness of the result obtained, some numerical examples are presented.