New linear binary block codes for the AWGN channel

We study the design of linear binary block codes exhibiting large minimum distance, i.e., suitable for the AWGN channel. It is first shown that the n columns of length 2^k of any (n, k) linear, binary block code, are also columns of a linear 2^k Hadamard matrix. Based on this observation, we develop nested search methods to obtain linear binary block codes of almost any practical rate having large minimum distance. The codes compare favorably with upper and lower bounds on the minimum distance, as well as to existing codes.