(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 a H a al a2 a3 a4 a5 a6 a7 a8aa10 a11 q12 a13 a14 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 Show that this code is capable of correcting single and two adjacent bit errors. Explain find the decoding algorithm. (Hint: Assuming the error vector has two consecutive ls, the syndrome)