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Unformatted text preview: ECE 635 Dr. N. El Naga Page 2 3.6 Suppose the minimum weight of an (n,k) code C is d. Prove that every combination of d - 1 or fewer columns of the parity check matrix H of C is linearly independent. Also prove that there exists at least one combination of d columns of H which is linearly dependent. 3.7 Let H be the parity check matrix for an (n,k) linear code C which has odd minimum weight d. Construct a new code C 1 whose parity check matrix is: | 0 | 0 | 0 H 1 = H | . | . | 0 1 1 1 1. . . | 1 (a) Prove that C 1 is an (n + 1,k) code. (b) Prove that every code vector in C 1 has even weight. (c) Prove that the minimum weight of C 1 is d + 1....
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- Spring '09
- #, Coding theory, Hamming Code, 0 g, parity check matrix, Dr. N. El Naga