Basics of finite fields: Groups, rings, fields, polynomials, field extensions, characterization of finite fields, roots of irreducible polynomials, traces, norms, bases, roots of unity, cyclotomic polynomials, representation of elements of finite fields, Wedderburn's theorem, order of polynomials, primitive polynomials, construction of irreducible polynomials, linearized polynomials, binomials, trinomials.;Applications to algebraic coding theory: Linear codes, cyclic codes, Goppa codes.
Rudolf Lidl & Harald Niederreiter, Finite Fields, Press, , 1997.
Steven Roman, Coding and Information Theory, Springer Verlag, 1992.
R. Lidl and H. Niederreiter, Introduction to finite fields and their applications, Cambridge University Press, 1986, Chapters 1-3 and 8.