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Abstract Let q be a power of a prime and F q be a finite field with q elements. In this paper, we propose four families of infinite classes of permutation trinomials having the form c x − x s + x q s , and investigate the relationship between two types of widely discussed permutation polynomials. Based on this relation, many classes of permutation polynomials having the form (x q k − x + δ) s + c x without restriction on δ are derived. [ABSTRACT FROM AUTHOR]

Let p be an odd prime, and m , k be positive integers with m ≥ 3 k . Let C 1 and C 2 be cyclic codes over F p with parity-check polynomials h 2 ( x ) h 3 ( x ) and h 1 ( x ) h 2 ( x ) h 3 ( x ) , respectively, where h 1 ( x ) , h 2 ( x ) and h 3 ( x ) are the minimal polynomials of γ − 1 , γ − ( p k + 1 ) and γ − ( p 3 k + 1 ) over F p , respectively, for a primitive element γ of F p m . Recently, Zeng et al. (2010) obtained the weight distribution of C 2 for m gcd ( m , k ) being odd. In this paper, we determine the weight distribution of C 1 , and the weight distribution of C 2 for the case that m gcd ( m , k ) is even. [ABSTRACT FROM AUTHOR]