Question

4. The Hamming (4, 7)-code is defined by means of the parity check matrix H and/or the generator matrix G, where H = [0 0 0 1 1 1 1; 0 1 1 0 0 1 1; 1 0 1 0 1 0 1], G = [1 0 0 0 0 1 1; 0 1 0 0 1 0 1; 0 0 1 0 1 1 0; 0 0 0 1 1 1 1]. (a) Encode the vector u = (1 1 0 0); (b) Decode the vectors v = (1 0 1 1 0 1 0) and w = (0 0 0 0 1 1 1). (c) Find all strings of length 7 which are decoded to (1 1 0 0).

          4. The Hamming (4, 7)-code is defined by means of the parity check matrix H and/or the generator matrix G, where
H = [0 0 0 1 1 1 1; 0 1 1 0 0 1 1; 1 0 1 0 1 0 1], G = [1 0 0 0 0 1 1; 0 1 0 0 1 0 1; 0 0 1 0 1 1 0; 0 0 0 1 1 1 1].
(a) Encode the vector u = (1 1 0 0);
(b) Decode the vectors v = (1 0 1 1 0 1 0) and w = (0 0 0 0 1 1 1).
(c) Find all strings of length 7 which are decoded to (1 1 0 0).

4. The Hamming (4, 7)-code is defined by means of the parity check matrix H and/or the generator matrix G, where
H = [0 0 0 1 1 1 1; 0 1 1 0 0 1 1; 1 0 1 0 1 0 1], G = [1 0 0 0 0 1 1; 0 1 0 0 1 0 1; 0 0 1 0 1 1 0; 0 0 0 1 1 1 1].
(a) Encode the vector u = (1 1 0 0);
(b) Decode the vectors v = (1 0 1 1 0 1 0) and w = (0 0 0 0 1 1 1).
(c) Find all strings of length 7 which are decoded to (1 1 0 0).

Added by Jose Ignacio R.

Advanced Engineering Mathematics

Dennis G. Zill, Warren S. Wright 5th Edition

Chapter 8

Instant Answer

Solved by Expert Sri K

03/11/2023

Step 1

The generator matrix G can be derived from the parity check matrix H. For a Hamming (4,7)-code, H is a 3x7 matrix, and G is a 4x7 matrix. The relationship between H and G is given by: H * G^T = 0 (mod 2) We are given the parity check matrix H: H = [1 1 1 0 0 0 Show more…

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The Hamming (4,7)-code is defined by means of the parity check matrix H and/or the generator matrix G, where H = [0 0 0 1 1 1 1; 0 1 1 0 0 1 1; 1 0 1 0 1 0 1], G = [1 0 0 0 0 1 1; 0 1 0 0 1 0 1; 0 0 1 0 1 1 0; 0 0 0 1 1 1 1]. (a) Encode the vector u = (1 1 0 0); (b) Decode the vectors v = (1 0 1 1 0 1 0) and w = (0 0 0 0 1 1 1). (c) Find all strings of length 7 which are decoded to (1 1 0 0).