Reed-Solomon codes. (a) Encoding. Suppose we want to encode the data vector =(7,6,5,4,3)F115 using the evaluation points =(0,1,2,3,4,5,6)F117. Find the encoding = f()F117 (b) Decoding in the presence of errors. Suppose that =(1,2,3,4,5,6)F136 and that =(3,8,6,0,7,1)F136. Find the unique polynomial fF13[x] of degree at most 1 such that f() agrees with in all but at most 2 coordinates, or conclude that no such f exists. Hints: For part (a), we have f=7+6x+5x2+4x3+3x4F11[x],d=4, and e=7. For part (b), we have d=1 and e=6. One possibility to decode is to try out all polynomials f of degree at most 1 over F13. How many such polynomials are there? Another is to use Gao's algorithm