EECS 376 Lecture Notes - Lecture 5: Aak, Singleton Bound

• School: U of M
• Department: Electrical Engineering And Computer Science
• Course: EECS 376
• Professor: Martin Strauss

Document Summary

We received the following: x r(x) = p(x) + e(x) Via an error-locator polynomial (a polynomial from whose roots we can nd the location of errors in the received codeword) or otherwise, we determine that the error is in the rst place. We know that the original polynomial p(x) is of the form p(x) = a + bx + cx2. Subtracting equation 2 from equation 3, we get that b = 1. Subtracting equation 2 from equation 1, we get 2c = 4 = c = 2. Substituting c = 2 into equation 2, we get that a + 4 = 4 = a = 0. So, we have a = 0, b = 1, and c = 2. Thus, we recover the original polynomial p(x) = 0 + x + 2x2: encode example. We can check our work above by encoding. We are given the polynomial p(x) = 0 + 1x + 2x2.