Thank you for your help. I need a solution of this problem ASAP. (AMS351 Book : Numbers, Groups & Codes six edition by Hemphreys & Prest)
Generator Matrix:
A generator matrix is a matrix whose rows form a basis for a linear code. The code words are all of the linear combinations of the rows of this matrix, that is, the linear code is the row space of its generator matrix.
Generator matrix G of C is a matrix whose rows generate all the elements of C, i.e., if G=(g1,g2,g3,...gk), then every codeword w of C can be represented as
w=c1g1+c2g2+c3g3+.........+ckgk)= cG
in a unique way, where c= (c1,c2,c3,.....ck)
Coset decoding table for generator matrix:
1 0 01 1 0
0 1 0 1 0 1
0 0 1 0 1 1
Parity check matrix:
0 1 1 0 0 1
1 0 1 0 1 0
1 1 0 1 0 0
Syndrome |
Coset |
000 |
0 |
001 |
e6 |
010 |
e5 |
011 |
e1 |
100 |
e4 |
101 |
e2 |
110 |
e3 |
111 |
e1+e4, e2+e5, e3+e6 |
v = c + e, where c is the codeword transmitted, and e is the error vector.
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