# Course

## M463 - Finite Fields

Course No:
M463
Credit:
4
Prerequisites:
M307
Approval:
2014
UG-Elective
Syllabus:
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.
Reference Books:
1. R. Lidl, H. Neiderreiter, “Finite Fields”, Cambridge university press, 2000.
2. G. L. Mullen, C. Mummert, “Finite Fields and Applications”, American Mathematical Society, 2007.
3. A. J. Menezes et. al., “Applications of Finite Fields”, Kluwer Academic Publishers, 1993.
4. Z-X. Wan, “Finite Fields and Galois Rings”, World Scientific Publishing Co., 2012.