The Reed$-$Solomon code that was used in the Voyager $2$ satellite when it transmitted images of Uranus back to Earth was the $16-$error correcting code that results from the primitive polynomial p$($x$)=$x$^8+$x$^4+$x$^3+$x$^2+1$ in Z$\_2[$x$].$ Construct several of the polynomial codewords in this code, and then illustrate the Reed$-$Solomon error correction method in this code by correcting several received polynomials that contain errors. Write a summary of your results. Include in your summary the total number of codewords in this code, the length of the binary vectors that correspond to the codewords in the code, and, provided that only one error burst occurs during transmission of the binary equivalent of a polynomial codeword in the code, the minimum the of binary errors that the code would be guaranteed to correct? What is the maximum number of binary errors that the code could correct?