Construction of Irreducible Polynomials over F5 and F7

Resumen

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 F^∗_5ⁿ and F^∗_7ⁿ in terms
of conjugate elements. Further, a technique to generate degree n irreducible polynomials over
F₅ and F₇ is also developed.