# Some new binary codes with improved minimum distances

A binary linear [n, k, d] code is a k-dimensional subspace of GF(2)$$^n$$, where n is the block length, k the dimension of the code, and d is the minimum distance between any two codewords. The minimum distance determines the error-correcting or error-detecting capability. Therefore, for a given block length n and dimension k, it is desired to have an [n, k, d] code with the minimum distance as large as possible. One of the most fundamental problems in coding theory is to construct codes with the best possible minimum distances.