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Though it is well known that the roots of any affine polynomial over a finitefield can be computed by a system of linear equations by using a normal base ofthe field, such solving approach appears to be difficult to apply when thefield is fairly large. Thus, it may be of great interest to find an explicitrepresentation of the solutions independently of the field base. This waspreviously done only for quadratic equations over a binary finite field. Thispaper gives an explicit representation of solutions for a much wider class ofaffine polynomials over a binary prime field.

Solutions of $x^{q^k}+\cdots+x^{q}+x=a$ in $GF{2^n}$