Orthogonality of a Generator Matrix of a Binary Block Code
Please see the attached file for the fully formatted problems.
4. Let be the generator matrix of a binary block code .
a) Show that each row of G is orthogonal to itself and to each of the other rows of G.
b) Show that each codeword in is orthogonal to itself and to every other codeword in .
Note: Use part a) and the fact that each codeword is a linear combination of the rows of G.
c) What is the dimension of ? Explain
d) What is the dimension of ? Explain
e) Show that is a self-dual code, that is show that = .
Can you explain what does orthogonally means and self-dual code?