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hw-2-2009 - zero and 2 m-1 only • 4 If a code has an...

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ECE 556: Coding Theory, 2009 Issued: September 15th, 2009 September 17, 2009 1) Prove the following bound on the size of the code: For a code with n < 2 d , it holds that M 2 b d 2 d - n c . 2) Show that the only two families of binary codes that meet the Singleton bound are the single parity-check and the repetition codes. 3) Show that the simplex [2 m - 1 ,m, 2 m - 1 ] codes have codewords of weight
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Unformatted text preview: zero and 2 m-1 only. • 4) If a code has an invertible generator matrix, what type of codes are there? • 5) Show that the Hamming distance obeys the triangle inequality. • 6) Show that in a linear binary code, either all the codewords begin with zero, or exactly half begin with one and half begin with zero. 1...
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