Construction of irreducible polynomials hold significant importance in coding theory, complexity theory and cryptography. Irreducible polynomials also helps us to generate non-zero elements of finite fields. In the present work, starting from a specified n degree irreducible polynomial, the methods to construct irreducible polynomials with a degree 6n over finite field F3s are explored. Additionally, a method for generating irreducible polynomial of degree p2n over finite field Fps by polynomial composition under specific constraints related to coefficients and the degree of initial irreducible polynomial is given.
Singh et al. (Wed,) studied this question.