Adv Alegbra HW Solutions 141

# Adv Alegbra HW Solutions 141 - 141 Solution. Absent. (ii)...

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141 Solution. Absent. (ii) Prove that | B r ( u ) |= r X i = 0 ³ n i ´ ( q 1 ) i . Solution. Absent. (iii) ( Gilbert-Varshamov bound . )I f C A n is an ( n , M , d ) -code, where | A |= q , prove that q n d 1 i = 0 ( n i ) ( q 1 ) i M . Solution. Absent. 4.70 ( Hamming bound )If C A n is an ( n , M , d ) -code, where | A |= q and d = 2 t + 1, prove that M q n t i = 0 ( n i ) ( q 1 ) i . Solution. Absent. 4.71 Prove that the Hamming [ 2 ` 1 , 2 ` 1 ` ] codes in Example 4.113 are perfect codes. Solution. Absent. 4.72 Suppose that a code C detects up to s errors and that it corrects up to t errors. Prove that t s . Solution. Absent. 4.73 If C F n is a linear code and w F n ,de f ne r = min c C δ(w, c ) .G ive an example of a linear code C F n , which corrects up to t errors, and a word w F n with w/ C , such that there are distinct codewords c , c 0 C with δ(w, c ) = r = δ( x , c 0 ) . Conclude that correcting a transmitted word
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## This note was uploaded on 12/21/2011 for the course MAS 4301 taught by Professor Keithcornell during the Fall '11 term at UNF.

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