On permutation and complete permutation binomials and trinomials from linearized polynomials over finite fields

In recent years, researchers have shown considerable interest in linearized polynomials and permutation polynomials over finite fields primarily because of their wide-ranging applications in fields such as cryptography, coding theory and communications theory. With their compact algebraic form and remarkable properties, permutation binomials and trinomials find extensive applications in the realms of mathematics and engineering. In this paper, we present a class of linearized polynomials over finite fields to construct permutation and complete permutation binomials and trinomials over F-p(n) subject to certain conditions.