18.310 Exam #1: Take Home Part
Due Tuesday, October 16, 2007, on Stellar
Problem 1. 10 points
Find a primitive polynomial p(x) of degree 6 which is not 1 + x + x6, and construct its remainder table.
Problem 2. 10 points
Find the polynomial p3(x) associated with the polynomial you chose in problem 1.
Problem 3. 40 points
Construct an encoder and decoder spreadsheet for the two-error-correcting BCH code associated with this polynomial. It should:
Have a place to enter the appropriate length message.
Create an encoded message from it.
Allow introduction of errors.
Compute t1 and t3 from the encoded message by using the appropriate remainder tables.
Compute the error locator polynomial from t1 and t3 and the appropriate tables.
Compute the locations of the errors and correct up to two errors.
Find the original message by dividing the corrected message by the encoding polynomial.