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 errorcorrecting
codes.
Part I.
Introduction to BSC, BEC, and information theory. Linear Codes, standard
array, maximum likelihood decoding, distance bounds, generator & parity
check matrices, errorsyndrome 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 errorcorrecting codes. Shor's and Grover's
algorithms.
Text:
There is no specific text. Students will
be given reading assignments from various references.
Supplementary Reading Material
from:

Berlekamp, Elwyn R., "Algebraic Coding Theory,"
McGrawHill, New York (1968)

Braunstein, Samuel L.,
Quantum Computation Tutorial
to be found at: http://chemphys.weizmann.ac.il/~schmuel/comp/comp.html

Gill, Arthur, "Linear Sequential Circuits,"
McGrawHill, New York (1966).

Hill, Raymond, "A First Course in Coding Theory,"
Oxford University Press, New York (1993).

Lomonaco, Samuel J., Jr.,
Lecture Notes
to be found at http://www.cs.umbc.edu/~lomonaco/lecturenotes/index.html

MacWilliams, F.J., and N.J.A. Sloane, "The Theory
of ErrorCorrecting Codes," NorthHolland Publishing Company, New York
(1977)

Peterson, W. Wesley, and E.J. Weldon, Jr., "ErrorCorrecting
Codes," MIT Press, Cambridge (1986).

Pless, Vera, "Introduction to the Theory of ErrorCorrecting
Codes," John Wiley (1982)

Preskill, John,
Lecture Notes
to be found at: http://www.theory.caltech.edu/people/preskill/ph229/#lecture

Roman, Steven, "Coding and Information Theory,"
SpringerVerlag, New York (1992).

Williams, Colin P., and Scott H. Clearwater,
"Explorations in Quantum Computing," SpringerVerlag, New York (1997).

Los Alamos Archive on
Quantum Physics
to be found at: http://xxx.lanl.gov/archive/quantph

Stanford Quantum Computation
Archive
to be found at: http://feynman.stanford.edu/qcomp/

Journal papers on shift registers and linear sequential
circuits

Journal papers on quantum errorcorrecting codes

Other references to be supplied later
Grading:
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