Abstract
AbstractAn irreducible polynomial can be derived in a stochastic way by examining the irreducibility of randomly generated polynomials. On the other hand, a systematic method of derivation for the irreducible polynomial has recently been introduced by presenting a class of irreducible polynomials of particular forms.This paper shows clearly that a higher‐order irreducible polynomial can be derived by applying a suitable variable transformation to the given irreducible polynomial. It is shown also that, when an irreducible polynomial is given where the coefficient is the element of a finite field with odd prime characteristic, an infinite number of higher‐order irreducible polynomials can be derived from that polynomial. A precise algorithm for the derivation is shown.
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