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In this paper, an idea of the cutting plane method is employed to improve thefractional distance of a given binary parity check matrix. The fractionaldistance is the minimum weight (with respect to l1-distance) of vertices of thefundamental polytope. The cutting polytope is defined based on redundant rowsof the parity check matrix and it plays a key role to eliminate unnecessaryfractional vertices in the fundamental polytope. We propose a greedy algorithmand its efficient implementation for improving the fractional distance based onthe cutting plane method.

A Cutting Plane Method based on Redundant Rows for Improving Fractional Distance