# Math 5251: Error-Correcting Codes and Finite Fields

## Spring 2006

Homework/exam schedule and assignments (tentative)
Assignment or Exam Due date Problems, mainly from Garrett's book
Homework 1 Wed Feb. 1 From Garrett's text:
1.33
2.02, 2.04, 2.05
3.02,3.05,3.06, (3.07 optional)

Not from text:
A. Consider these three collections C1, C2, C3 of codewords:
C1={0,10,110,1110,1111}
C2={0,10,110,1110,1101}
C3={0,01,011,0111,1111}
Indicate for each (with explanation) whether or not it is
(a) uniquely decipherable,
(b) instantaneous.

B. Does there exist a binary code which is instantaneous and has code words with lengths (1,2,3,3)? If not, prove it. If so, construct one.

C. State and prove the precise conditions under which a random variable X on a finite probability space has entropy H(X) equal to zero.
Homework 2 Wed Feb. 15 From Garrett's text:
4.01, 4.02, 4.04, 4.06, (4.07 removed from HW), 4.11, 4.12

Not from text:
Let p be a probability between 0 and 1.
Explain why a noisy channel with input and output alphabets both {0,1} and the following probabilities is called a useless channel:
Midterm exam 1 Wed. Feb. 22 Midterm exam 1 in PostScript, PDF.
Homework 3 Wed Mar. 8 From Garrett's text:
5.01, 02, 03, 04, 05, 08
6.01, 02, 05, 20, 22, 38, 48, 50, 53
Homework 4 Wed Mar. 29 From Garrett's text:
6.30, 31, 57, 81
8.17
9.11, 12
10.04, 08, 09, 11, 13
11.11
12.06, 12.10, 12.12, 12.14, 12.15
Midterm exam 2 Wed. Apr. 5 Midterm exam 2 in PostScript, PDF.
Homework 5 Wed Apr. 19 From Garrett's text:
12.01, 04, 17, 19, 20
13.02, 05, 07, 09, 10
14.01, 04
Homework 6 Wed Apr. 26 (note 1-week due date!) From Garrett's text:
11.02, 05, 07
15.03, 13
16.05
Final exam Wed. May 3 Final exam in PostScript, PDF.