Third Assignment: due Fri. Mar 9
- CT 3.1.11 codewords with k zeros (over an arbitrary field).
- a. Find a code with minimum distance d = 5 , redundancy
r = n - k = 8 and length n as large as
b. Compare your result with the Gilbert-Varshimov bound.
c. Do the same for r = 9 if you want to impress me.
- CT 3.3.10, decoding for a Hamming code.
- CT 3.4.4, SDA for decoding an extended Hamming code.
- CT 3.4.5, extended Hamming code is self dual.
- Write down a parity check matrix for the ternary Hamming code with
redundancy r = 3.
- CT 3.5.2, another generator for the Golay code.
- CT 3.5.3, Golay code is self dual.
- CT 3.6.5 f, g, h, i, decoding for the extended Golay code.
- Find the number of codewords of each possible weight, 0,1,..,24
for the binary extended Golay code (CT 3.7.7-9).
- a. What is the difference between puncturing a code and shortening
b. Use the ternary Golay code to illustrate the difference
by puncturing and shortening with respect to the last coordinate.
The ternary Golay has matrix [I_6 A] where
c. Which of the two, the shortened Golay or the punctured Golay, is perfect?