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A class of bilinear permutation polynomials over a finite field ofcharacteristic 2 was constructed in a recursive manner recently which involvedsome other constructions as special cases. We determine the compositionalinverses of them based on a direct sum decomposition of the finite field. Theresult generalizes that in [R.S. Coulter, M. Henderson, The compositionalinverse of a class of permutation polynomials over a finite field, Bull.Austral. Math. Soc. 65 (2002) 521-526].

The compositional inverse of a class of bilinear permutation polynomials over finite fields of characteristic 2