Question

Problem 1. Determine the length, the size, and the minimal distance for each q-ary code C below. How many errors can each code correct? detect?

(a) C = { (0, 0, 0, 0, 0, 0), (0, 1, 1, 1, 1, 0), (1, 0, 0, 0, 0, 1), (1, 1, 1, 1, 1, 1) }. Here q = 2.

(b) C = { (0, 0, 0, 0, 0, 0, 0), (2, 1, 0, 2, 1, 0, 1), (2, 2, 2, 2, 2, 2, 2) }. Here q = 3.

(c) C = { (0, 1, 2, 3, 4), (1, 2, 3, 4, 0), (2, 3, 4, 0, 1), (3, 4, 0, 1, 2), (4, 0, 1, 2, 3) }. Here q = 5.

Problem 2. Assume the code from Problem 1(a) was used in transmission, and the following words were received. Decode each of these words using the nearest neighbour decoding algorithm. (The incomplete decoding version: if there is more than one nearest neighbour, declare an error.)

(a) (0, 1, 0, 0, 0, 0),

(b) (1, 1, 0, 0, 1, 1),

(c) (0, 1, 0, 1, 0, 1),

(d) (1, 1, 0, 0, 0, 0).

Answer 1