[SOLVED] CS MATH 3320 Spring 2021

MATH 3320 Spring 2021
Problem Set 2
Due Thursday February 11 at 11:59 pm Nashville time
Instructions: The solution for each problem number (1,2,3,etc.) should be written on its own sheet of paper. Scan the solutions into a single PDF. Upload your solutions to Gradescope under the correct assignment. Make sure each page is matched to the correct problem on Gradescope.
(Problem numbers from the textbook are the same in both editions.)
1. Bierbrauer 1.5.1
2. What does the sphere-packing bound tell us about the number of codewords in a ternary code
with length 5 minimum distance 3?
3. Bierbrauer 1.6.2
4. Bierbrauer 1.6.5
5. Bierbrauer 1.6.8
6. Bierbrauer 2.1.1
7. Bierbrauer 2.1.5
8. i. Show that
(You may assume that no code (5, 5, 3)2 exists.)
1 0 1 1 1 G=1 1 1 0 0
01110
is a generator matrix of a binary linear code C of dimension 3.
ii. Construct a bijective, linear encoding function : F32 C. (List (x) for each vector x in F32.)