4. (6 points) A (15,10) binary cyclic code has 1 and a as the roots of the generator polynomial, where a is a primitive root of GF(24). The corresponding H matrix can be written as 12 a 14 H = 20 1 al a2 a3 a4 1 1 1 1 a5 1 a 6 1 a7 1 a8 1 a 1 a 10 1 a11 1 a 13 1 1 1 Show that this code is capable of correcting single and two adjacent bit errors. Explain the decoding algorithm. (Hint: Assuming the error vector has two consecutive ls, find the syndrome)