Homework Statement
What is the maximum allowable probability of error is a typical digit in order that the (8, 4) Hamming Code can be used with probability .999 that the receiver will not be misled (i.e., 3 or more errors occur) in a single word?
Homework Equations...
Homework Statement
Let F be the 4x4 matrix whose (i, j)th entry is 5ij in F_13 for i, j = 0,1,2, 3.
Compute F(hat) and verify that F(hat)F = I
Homework Equations
The matrix F(hat) is called the inverse discrete Fourier transform of F.
The Attempt at a Solution
I found that e = 4...
That was my original question stated above. I do not understand how to write down F and wanted to see if anyone knew how to come up with the matrix for F so then I can easily obtain F(hat).
1. F_13 is a field of 13 elements.
2. My apologies, I meant to write 5^(ij).
3. I already defined that above. The matrix F(hat) is called the inverse discrete Fourier transform of matrix F.
Homework Statement
(i) Verify that 5 is a primitive 4th root of unity in F13.
(ii) Let F be the 4x4 matrix whose (i, j)th entry is 5ij in F13 for i, j = 0,1,2, 3.
Compute F(hat) and verify that F(hat)F= I.
Homework Equations
The matrix F(hat) is called the inverse discrete Fourier...
Homework Statement
For polynomials f(x),g(x) of degree d = 2(r−1)−1, check that multiplying f(x) and g(x) by the Karatsuba method requires 3(r-1) multiplications in the field F.
Homework Equations
You can can more clearly see problem on page 383 #10...
Homework Statement
In F17, 2 is a primitive 8th root of unity. Evaluate f(x) = 7x3+8x2+3x+5 at the eight powers of 2 in F17. Verify that the method requires at most 16 multiplications in F17. Homework Equations
You can can more clearly see the theorem on page 376-378 and the problem is on page...