On certain projective geometry codes (Corresp.)

Let be an binary projective geometry code with , and . This code is -step majority-logic decodable. With reference to the GF , the generator polynomial , of , has as a root if and only if has the form and , where indicates the weight of the radix- representation of the number . Let be the set of nonzero numbers , such that is a root of . Let be the cyclotomic cosets such that is the union of these cosets. It is clear that the process of finding becomes simpler if we can find a representative from each , since we can then refer to a table, of irreducible factors, as given by, say, Peterson and Weldon. In this correspondence it was determined that the coset representatives for the cases of , with , and , with .