A CONSIDERATION FOR DERIVING NONBINARY IRREDUCIBLE POLYNOMIALS

An irreducible polynomial can be derived in a stochastic way by examin ing the irreducibility of randomly generated polynomials. On the other hand, a systematic method of derivation for the irreducible polynomia l has recently been introduced by presenting a class of irreducible po lynomials of particular form. This paper shows clearly that a higher-o rder irreducible polynomial can be derived by applying a suitable vari able transformation to the given irreducible polynomial. It is shown a lso that, when an irreducible polynomial is given where the coefficien t is the element of a finite field with odd prime characteristic, an i nfinite number of higher-order irreducible polynomials can be derived from that polynomial. A precise algorithm for the derivation is shown.