Mathematics 5251 (Error-Correcting Codes, Finite Fields, Algebraic Curves)



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Required text: The Mathematics of Coding Theory, by Paul Garrett.

Homework: Weekly homework assignments are due on Monday of the following week in the beginning of class.

Exams: There will be two midterm exams on Wednesdays, March 5 and April 16, and a final exam on Monday, May 12, 4:00 -- 6:00, room to be announced.

Make up exams: Will be allowed only under truly exceptional circumstances. You must notify the lecturer at least a week in advance.

Calculators: Calculators are not permitted for the midterms and the final exam. A calculator will be useful for some of the homework problems.

Final grade: Homework counts for 40%, each of the midterm exams for 15% and the final exam for 30%.

Lecture date Homework assignment Due date
Week 1
Wednesday
January 22 		pp. 29 -- 30:
1.01 -- 1.14, 1.17, 1.21		 Monday
January 27
Monday
January 27 		classes canceled Monday
February 3
Wednesday
January 29 		pp. 30 -- 31:
1.28 -- 1.31, 1.33, 1.39, 1.40		 Monday
February 3
Monday
February 3 		pp. 31, 32:
1.42, 1.45, 1.48		 Monday
February 10
Wednesday
February 5 		p. 43:
2.01 -- 2.05		 Monday
February 10
Monday
February 10 		Read Sections 3.1, 3.2, and 3.3;
Exercises p. 60:
3.01, 3.02, 3.03		 Monday
February 17
Wednesday
February 12 		Read Sections 3.4, 4.1 and 4.2;
Exercises p. 60:
3.04 through 3.07
Exercises p. 80:
4.01 through 4.05		 Monday
February 17
Monday
February 17 		Read Sections 4.3, 4.4, and 4.5;
Exercises p. 81:
4.08, 4.09, 4.10, 4.11		 Monday
February 24
Wednesday
February 19 		Read Sections 5.1 through 5.4;
Exercises p. 92:
5.01 through 5.05, 5.07, 5.08		 Monday
February 24
Monday
February 24 		Read Sections 6.1, 6.2, 6.3, 6.5 and 6.7;
Exercises pp. 129-131:
6.02 -- 6.07, 6.19, 6.20, 6.37, 6.39 and:
Find the multiplicative inverse of 56 modulo 137		 Monday
March 3
Wednesday
February 26 		Read Sections 6.8 through 6.15;
Exercises pp. 132--133:
6.52, 6.53		 Monday
March 3
Monday
March 3 		Read Sections 10.1 -- 10.5;
Exercises pp. 131 -- 132:
6.50, 6.57 and:
Exercises p. 191:
10.11, 10.13 and:
Is 32 a primitive root modulo 101?
Find the multiplicative inverse of (x+1) modulo (x^3+x^2+1)		 Monday
March 10
Wednesday
March 5 		Solutions for midterm 1
Monday
March 10 		Read Sections 13.1
Exercises pp. 232 -- 233:
13.01, 13.02, 13.03
Read Section 12.4
Exercises p. 226:
12.01 and 12.02		 Monday
March 24
Wednesday
March 12 		Read Sections 12.5 -- 12.7
p. 226: Exercises 12.07, 12.09, 12.11, 12.13
 Monday
March 24
Monday
March 24 		Read Sections 13.2
Exercises p. 233:
13.04 -- 13.10
Read Section 12.6
Find a linear dependence relation for 1110, 1011, 1101, 0111 and 1111		 Monday
March 31
Wednesday
March 26 		Read Sections 12.7 -- 12.8
p. 227: Exercises 12.16 through 12.20
 Monday
March 31
Monday
March 31 		Read Sections 14.1 and 14.2
Exercises p. 238:
14.01 and 14.02
Monday
April 7
Wednesday
April 2 		Exercises pp. 238 -- 239:
14.03, 14.04 and 14.05
 Monday
April 7
Monday
April 7 		Read Section 10.3 and Sections 11.1 through 11.5
Exercises p. 198:
11.01 and 11.03
Is the polynomial $x^5+x+1$ irreducible in $(\mathbb Z/2)[x]$?
Monday
April 14
Wednesday
April 9 		Exercises p. 259:
15.01, 15.11 and 15.12
Read Section 17.3
Exercises p. 295:
17.07
 Monday
April 14
Monday
April 14 		Read Sections 17.1, 17.2 and 17.3
Exercises p. 295:
17.08, 17.09 and 17.10
Monday
April 21
Wednesday
April 16 		Solutions for midterm 2
Monday
April 21 		Read Sections 17.4 and 17.5 Monday
April 28
Wednesday
April 23 		pp. 295 -- 296:
17.11, 17.12 and 17.13 		Monday
April 28
Monday
April 28 		Read Sections 19.7 and 19.8 Monday
May 5
Wednesday
April 30 		How many irreducible polynomials of degree 12 with coefficients in $\mathbb F_2$ are there?
How many primitive polynomials of degree 5 with coefficients in $\mathbb F_3$ are there? 		Monday
May 5
Monday
May 5 		prepare for the final exam
Wednesday
May 7 		prepare for the final exam
Final exam Monday May 12, 4:00 -- 6:00, regular classroom.