CMSC 653: Coding Theory & Applications

Instructor: S.J. Lomonaco, Jr.

Spring 1998

Course Description:

The course will consists of two parts, the first part on algebraic coding theory, the second part on quantum error-correcting codes.

Part I. Introduction to BSC,  BEC, and information theory. Linear Codes, standard array, maximum likelihood decoding, distance bounds, generator & parity check matrices, error-syndrome table. A brief overview of rings and ideals.  Cyclic codes, generator & parity check polynomials, linear sequential circuits (LSCs), implementation of cyclic codes in terms of LSCs.  Finite fields, applications of finite fields to cyclic codes.  BCH codes, the BCH decoding algorithm. A brief overview of convolutional codes.

Part II.  A quick overview of  quantum mechanics, quantum information theory, and quantum cryptography. Various quantum error-correcting codes. Shor's and Grover's algorithms.


There is no specific text.  Students will be given reading assignments from various references.

Supplementary Reading Material from:

  1. Berlekamp, Elwyn R., "Algebraic Coding Theory," McGraw-Hill, New York (1968)
  2. Braunstein, Samuel L., Quantum Computation Tutorial to be found at:
  3. Gill, Arthur, "Linear Sequential Circuits," McGraw-Hill, New York (1966).
  4. Hill, Raymond, "A First Course in Coding Theory," Oxford University Press, New York (1993).
  5. Lomonaco, Samuel J., Jr., Lecture Notes to be found at

  6. MacWilliams, F.J., and N.J.A. Sloane, "The Theory of Error-Correcting Codes," North-Holland Publishing Company, New York (1977)
  7. Peterson, W. Wesley, and E.J. Weldon, Jr., "Error-Correcting Codes," MIT Press, Cambridge (1986).
  8. Pless, Vera, "Introduction to the Theory of Error-Correcting Codes," John Wiley (1982)
  9. Preskill, John, Lecture Notes to be found at:

  10. Roman, Steven, "Coding and Information Theory," Springer-Verlag, New York (1992).
  11. Williams, Colin P., and Scott H. Clearwater, "Explorations in Quantum Computing," Springer-Verlag, New York (1997).
  12. Los Alamos Archive on Quantum Physics to be found at:
  13. Stanford Quantum Computation Archive to be found at:
  14. Journal papers on shift registers and linear sequential circuits
  15. Journal papers on quantum error-correcting codes
  16. Other references to be supplied later


The Course grade will be computed as follows:

	25%	Exam I
	25%	Exam II
	25%	Homework Avg
	25%	Final Exam

Prerequisites:CMSC 203, MATH 221, Reasonable Mathematical & Algorithmic Maturity, and an Intense Desire to Learn

Last Modified: January 27, 1998