Different logic synthesis tasks have been formulated as input encoding problems but restricted to use a minimun number of binary variables. This paper presents an original column based algorithm to solve this opmization problem. The new algorithm targets economical implementation of face constraints unlike conventional algorithms which do not care about infeasible ones. Experimental results that demonstrate the superiority of the new method versus conventional tools and a previous algorithm specifically developed for the minimum length encoding problem are shown. An state assignment tool which core is the new algorithm is evaluated by implementing an standard benchmark of sequential circuits. It compares very favorably to well known tools like NOVA.