Several classes of codes generated from orthogonal functions
Perng Hsieh, Mu-Yue Hsiao · IEEE Transactions on Information Theory · 1964
A method of designing codes from orthogonal functions utilizing the existing knowledge of discrete error-correcting binary codes is given. The method consists in constructing the transformation matrix,[a_{ij}], that performs the linear transformation by taking the finite set of orthogonal functions into the set of continuous code words. Several classes of code words are found whose transformation matrices[a_{ij}]use symbols0, -1, and1, and each row of which contains equal number of nonzero elements. They are better than the randomly found existing codes in the sense that with the same number of orthogonal functions and distance criterion, more code words can be obtained.