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Show that low-density generator-matrix codes are bad. A family of low-density generator-matrix codes is defined by two parameters j, k, which are the column weight and row weight of all rows and columns respectively of G. These weights are fixed, independent of N; for example, (j, k) = (3, 6). [Hint: show that the code has low-weight codewords, then use the argument from p.215.]
A sphere of radius R is uniformly charged to a total charge of Q. It is made to spin about an axis that passes through its center with an angular speed ω. Find the magnitude of the resulting magnetic field at the center of the sphere.
A resistor is in the shape of a cube, with each side of resistance R . Find the equivalent resistance between any two of its adjacent corners.
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