Fifth Assignment, Cyclic Codes: due Mon. Apr. 16
- CT 4.2.21: d.
- CT 4.3.4.
- CT 4.3.6: a.
- CT 4.3.8 (4.3.11 in the old edition).
- CT 4.3.9: e (4.3.12: e in the old edition).
Find the remainders when each x^i
is divided by g.
- CT 4.4.6: f,g.
- A study of binary cyclic codes of length 14.
a. Factor x^12+1 .
b. How many distinct cyclic codes of length 14 are there?
c. Describe concisely all possible codes by giving for each code:
d. What are the possible dimensions? How many codes are there for each dimension?
- the generator polynomial g(x) (You can leave it factored.),
- its dimension,
- the generator polynomial for the dual code.
e. There are three distinct codes of rate 1/2. For each one find
- the generator polynomial g(x)
- the generator polynomial for the dual code h¯(x)
- the generating matrix based on the generator polynomial,
- the matrix A such that
[A I] is a systematic encoding matrix, or equivalently
Transpose([I A]) is a parity check matrix.
- CT 4.5.5: g; this problem concerns the Golay code.