Orthogonality of binary codes derived from Reed-Solomon codes

The author provides a simple method for determining the orthogonality of binary codes derived from Reed-Solomon codes and other cyclic codes of length 2^m-1 over GF(2^m) for m bits. Depending on the spectra of the codes, it is sufficient to test a small number of single-frequency pairs for orthogonality, and a pair of bases may be tested in each case simply by summing the appropriate powers of elements of the dual bases. This simple test can be used to find self-orthogonal codes. For even values of m, the author presents a technique that can be used to choose a basis that produces a self-orthogonal, doubly-even code in certain cases, particularly when m is highly composite. If m is a power of 2, this technique can be used to find self-dual bases for GF(2 ^m). Although the primary emphasis is on testing for self orthogonality, the fundamental theorems presented apply also to the orthogonality of two different codes