Course

Course Summary
Credit Type:
Course
ACE ID:
NNCS-0670
Organization's ID:
MATH1110
Organization:
National Cryptologic University
Location:
Hybrid
Length:
16 hours
Dates Offered:
Credit Recommendation & Competencies
Level Credits (SH) Subject
Lower-Division Baccalaureate 2 Applications of Finite Fields
Description

Objective:

The course objective is to introduce basic concepts of the finite field number systems.

Learning Outcomes:

  • compute the Euclidean algorithm for integers;
  • recognize the properties of groups, rings, and integral domains;
  • construct prime finite fields;
  • compute characteristics of polynomials and their reverses;
  • perform the Division and Euclidean algorithm for polynomials;
  • recognize properties of extension fields;
  • produce finite fields using shift registers, primitive elements, and primitive polynomials;
  • identify minimal polynomials;
  • compute conjugates and cyclotomic cosets of a field;
  • construct finite fields to coding theory using the Peterson tables;
  • perform modulo arithmetic;

General Topics:

  • Division and Modulo arithmetic
  • Euclidean algorithm and division algorithms for integers and polynomials
  • Groups, rings, and integral domains
  • Prime finite fields and extension fields
  • Polynomials and minimal polynomials
  • Primitive elements and primitive polynomials
  • Logarithms
  • Conjugates and cyclotomic cosets
  • Peterson tables
Instruction & Assessment

Instructional Strategies:

  • Computer Based Training

Methods of Assessment:

  • Examinations
  • Quizzes

Minimum Passing Score:

70%
Supplemental Materials