A code C consists of all binary sequences of length 6 and weight 3. 1. Is this code a linear...

A code C consists of all binary sequences of length 6 and weight 3.

1. Is this code a linear block code? Why?

2. What is the rate of this code? What is the minimum distance of this code? What is the minimum weight for this code?

3. If the code is used for error detection, how many errors can it detect?

4. If the code is used on a binary symmetric channel with crossover probability of p, what is the probability that an undetectable error occurs? 5. Find the smallest linear block code C1 such that C ⊆ C1 (by the smallest code we mean the code with the fewest code words).