Structure of finite fields: characterization, roots of irreducible polynomials,traces, norms and bases, roots of unity, cyclotomic polynomial, representation of elements of finite fields, Wedderburn’s theorem; Polynomials over finite field: order of polynomials, primitive polynomials, construction of irreducible polynomials, binomials and trinomials, factorization of polynomials over small and large finite fields, calculation of roots of polynomials; Linear recurring sequences: LFSR, characteristic polynomial, minimal polynomial, characterization of linear recurring sequences, Berlekamp-Massey algorithm; Applications of finite fields: Applications in cryptography, coding theory, finite geometry, combinatorics.
- R. Lidl, H. Neiderreiter, “Finite Fields”, Cambridge university press, 2000.
- G. L. Mullen, C. Mummert, “Finite Fields and Applications”, American Mathematical Society, 2007.
- A. J. Menezes et. al., “Applications of Finite Fields”, Kluwer Academic Publishers, 1993.
- Z-X. Wan, “Finite Fields and Galois Rings”, World Scientific Publishing Co., 2012.