On the Study of Families of Linearized Polynomials over Finite Fields

Abstract

Linearized polynomials are gaining attention from many researchers because of their applications in the field of coding theory, cryptography and finite geometry. The linearized polynomials of the type T_l^k (Z) and S_l^k (Z) were recently introduced in the literature. The characterization of these linearized polynomials and patterns in their roots over finite fields have been extensively studied by various authors. In the present paper, we extend the study of families of linearized polynomials T_l^k (Z) and S_l^k (Z) by taking k and l as prime powers and construct new families of linearized polynomials over finite fields. Further, we establish relation between linearized polynomials T_l^k (Z) and S_l^k (Z) which may be helpful in determining zeros of these polynomials over finite fields.