Irreducibility of Some Composite Polynomials Over Finite Fields
Abstract
Given the field F with q elements and of characteristics p and an irreducible polynomial P(x) = cnxn+cn¡1xn¡1+c1xn¢¢¢c0 over F. We prove that the composite polynomial (dxp ¡ dx)n p ³ axp¡ax+c dxp¡dx ´ is irreducible over F under certain conditions. Also a recursive construction of sequences of irreducible polynomials of degree n2k(k = 1; 2; 3; ¢ ¢ ¢) over F2s is given.
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