PPT Slide

Hadamard Code

Hadamard Matrix M

• Entries are +1 or -1

• MMT = nIn (where In is the n x n identity matrix)

• There are infinitely many such matrices

Resulting Code

• a [2L, L , 2L-1]2 code

• How do you encode it? Table lookup will work...

• constant distance rate (that’s good) since lim as n gets large d/n = 2L-1 / 2L = .5

• exponentially dropping message rate (that’s bad) since lim k/n = L / 2L = 0

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