ABSTRACT

The cyclic structure is clearly visible. Addition of a parity check bit to each row of G yields a generator matrix of the so-called extended binary Golay code. It is easily checked that this code G24 is self-dual: G24=G24?. In fact, because of the cyclicity it suffices to check that the first row of the generator matrix is orthogonal to all rows. In fact cyclic codes are one of the most widely used families of codes. The traditional theory of cyclic codes uses notation and results from ring theory. A particularly important family of designs are the projective geometries. Design theory is an important branch of modern combinatorial theory. The basic axiom is a uniformity property reminiscent of the definition of orthogonal arrays. In fact one of the origins of combinatorial design theory is in statistics and in particular in the design of experiments.