Construction of Irreducible Polynomials over F₅ and F₇

Construction of irreducible polynomials is crucial because of their implications in formulating error correcting codes, linear feedback shift register designs and to study algebraic complexity of polynomials. Irreducible polynomials also help us to generate non-zero elements of finite fields. In this manuscript, we construct and characterize the structure of (Formula presented) in terms of conjugate elements. Further, a technique to generate degree n irreducible polynomials over F₅and F₇is also developed.