Non-constructive lower bounds for binary asymmetric error correcting codes
Parthe Pandit, Ankur A. Kulkarni · 2017
Lower bounds on maximum error correcting codes have commonly been obtained via code construction. In this paper we introduce a non-constructive approach for finding lower bounds for this problem. Recently, Pandit and Kulkarni [6] formulated the independence number of a graph as an l1maximization over the solution set of a linear complementarity problem (LCP) associated with the adjacency matrix of the graph. Using this formulation, we derive non-constructive lower bounds on the size of the largest code correcting binary asymmetric errors. Our approach facilitates lower bounds for multiple error correcting codes as well which are obtained by solving a linear system of equations of size less than the block-length. Our bound is tighter than the Caro-Wei bound, as is demonstrated empirically.