Linear Binary Error Correcting Codes with Specified Minimum Hamming Distance

Abstract

A procedure for generating liner binary codes with minimum hamming distance specified is given. The work involves the theoretical aspect in the form of two new theorems. Thus the details are restricted to small values of minimum distance. An outline of the procedure for larger values is discussed. The method relies on the fact that a linear binary code is a subspace of the vector space of all n-tuples. The construction of the code makes use of the properties of the gray code.