How to create generator matrix from given 8 linear codewords of (7,3). The Next CEO of Stack OverflowParity Check MatrixParity check matrix and error syndromesMatrix Generator,Coding TheoryGenerator matrix of a binary cyclic codeBuilding a generator matrixRow/Column operations of a parity check/generator matrix for a linear codeGiven binary codewords find generator matrixHow is a generator matrix built?Code$C$ over $Z_3$ given by the solutions of a linear system of equationsWhat will be the Generator Matrix for 4B/5B Linear Block code?
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How to create generator matrix from given 8 linear codewords of (7,3).
The Next CEO of Stack OverflowParity Check MatrixParity check matrix and error syndromesMatrix Generator,Coding TheoryGenerator matrix of a binary cyclic codeBuilding a generator matrixRow/Column operations of a parity check/generator matrix for a linear codeGiven binary codewords find generator matrixHow is a generator matrix built?Code$C$ over $Z_3$ given by the solutions of a linear system of equationsWhat will be the Generator Matrix for 4B/5B Linear Block code?
$begingroup$
Four codewords of a linear $(7,3)$ code $C$ are given to me in a question with no other details, which are$$0110101,1001101,1001011,0000000.$$I am asked to write down the missing codewords.
I have tried choosing generator matrix randomly but could not find the correct codewords. However i was able to find the correct codewords by using linear code word property of xor of two codewords will also be a codeword.
Now I have all eight codewords and want to make a generator matrix or parity matrix from given eight codewords but I am confused on how to create it. I have several documents but they seem to be using parity matrix which I do not have here.
coding-theory
edited Mar 19 at 22:07
Henno Brandsma
115k348124
asked Mar 19 at 12:25
Tahir AbbasTahir Abbas
62
$endgroup$
add a comment |
$begingroup$
Four codewords of a linear $(7,3)$ code $C$ are given to me in a question with no other details, which are$$0110101,1001101,1001011,0000000.$$I am asked to write down the missing codewords.
I have tried choosing generator matrix randomly but could not find the correct codewords. However i was able to find the correct codewords by using linear code word property of xor of two codewords will also be a codeword.
Now I have all eight codewords and want to make a generator matrix or parity matrix from given eight codewords but I am confused on how to create it. I have several documents but they seem to be using parity matrix which I do not have here.
coding-theory
edited Mar 19 at 22:07
Henno Brandsma
115k348124
asked Mar 19 at 12:25
Tahir AbbasTahir Abbas
62
$endgroup$
add a comment |
$begingroup$
Four codewords of a linear $(7,3)$ code $C$ are given to me in a question with no other details, which are$$0110101,1001101,1001011,0000000.$$I am asked to write down the missing codewords.
I have tried choosing generator matrix randomly but could not find the correct codewords. However i was able to find the correct codewords by using linear code word property of xor of two codewords will also be a codeword.
Now I have all eight codewords and want to make a generator matrix or parity matrix from given eight codewords but I am confused on how to create it. I have several documents but they seem to be using parity matrix which I do not have here.
coding-theory
edited Mar 19 at 22:07
Henno Brandsma
115k348124
asked Mar 19 at 12:25
Tahir AbbasTahir Abbas
62
$endgroup$
Four codewords of a linear $(7,3)$ code $C$ are given to me in a question with no other details, which are$$0110101,1001101,1001011,0000000.$$I am asked to write down the missing codewords.
I have tried choosing generator matrix randomly but could not find the correct codewords. However i was able to find the correct codewords by using linear code word property of xor of two codewords will also be a codeword.
Now I have all eight codewords and want to make a generator matrix or parity matrix from given eight codewords but I am confused on how to create it. I have several documents but they seem to be using parity matrix which I do not have here.
coding-theory
coding-theory
edited Mar 19 at 22:07
Henno Brandsma
115k348124
asked Mar 19 at 12:25
Tahir AbbasTahir Abbas
62
edited Mar 19 at 22:07
Henno Brandsma
115k348124
asked Mar 19 at 12:25
Tahir AbbasTahir Abbas
62
edited Mar 19 at 22:07
Henno Brandsma
115k348124
edited Mar 19 at 22:07
Henno Brandsma
115k348124
edited Mar 19 at 22:07
Henno Brandsma
115k348124
115k348124
asked Mar 19 at 12:25
Tahir AbbasTahir Abbas
62
asked Mar 19 at 12:25
Tahir AbbasTahir Abbas
62
asked Mar 19 at 12:25
Tahir AbbasTahir Abbas
62
62
add a comment |
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
The first three words are linearly independent over $Bbb Z_2$. This allows you to write down a $3times 7$ generator matrix $G$ with the codewords as rows.
Then you find the code as $C = aGmid ainBbb Z_2^3$.
answered Mar 19 at 12:30
WuestenfuxWuestenfux
5,3331513
$endgroup$
$begingroup$
would not it create a 3 x 7 generator matrix?
$endgroup$
– Tahir Abbas
Mar 19 at 12:54
$begingroup$
Sorry, a typing error.
$endgroup$
– Wuestenfux
Mar 19 at 13:06
add a comment |
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1 Answer
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oldest
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1 Answer
1
active
oldest
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oldest
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active
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votes
$begingroup$
The first three words are linearly independent over $Bbb Z_2$. This allows you to write down a $3times 7$ generator matrix $G$ with the codewords as rows.
Then you find the code as $C = aGmid ainBbb Z_2^3$.
answered Mar 19 at 12:30
WuestenfuxWuestenfux
5,3331513
$endgroup$
$begingroup$
would not it create a 3 x 7 generator matrix?
$endgroup$
– Tahir Abbas
Mar 19 at 12:54
$begingroup$
Sorry, a typing error.
$endgroup$
– Wuestenfux
Mar 19 at 13:06
add a comment |
$begingroup$
The first three words are linearly independent over $Bbb Z_2$. This allows you to write down a $3times 7$ generator matrix $G$ with the codewords as rows.
Then you find the code as $C = aGmid ainBbb Z_2^3$.
answered Mar 19 at 12:30
WuestenfuxWuestenfux
5,3331513
$endgroup$
$begingroup$
would not it create a 3 x 7 generator matrix?
$endgroup$
– Tahir Abbas
Mar 19 at 12:54
$begingroup$
Sorry, a typing error.
$endgroup$
– Wuestenfux
Mar 19 at 13:06
add a comment |
$begingroup$
The first three words are linearly independent over $Bbb Z_2$. This allows you to write down a $3times 7$ generator matrix $G$ with the codewords as rows.
Then you find the code as $C = aGmid ainBbb Z_2^3$.
answered Mar 19 at 12:30
WuestenfuxWuestenfux
5,3331513
$endgroup$
The first three words are linearly independent over $Bbb Z_2$. This allows you to write down a $3times 7$ generator matrix $G$ with the codewords as rows.
Then you find the code as $C = aGmid ainBbb Z_2^3$.
answered Mar 19 at 12:30
WuestenfuxWuestenfux
5,3331513
edited Mar 19 at 13:06
answered Mar 19 at 12:30
WuestenfuxWuestenfux
5,3331513
answered Mar 19 at 12:30
WuestenfuxWuestenfux
5,3331513
answered Mar 19 at 12:30
WuestenfuxWuestenfux
5,3331513
5,3331513
$begingroup$
would not it create a 3 x 7 generator matrix?
$endgroup$
– Tahir Abbas
Mar 19 at 12:54
$begingroup$
Sorry, a typing error.
$endgroup$
– Wuestenfux
Mar 19 at 13:06
add a comment |
$begingroup$
would not it create a 3 x 7 generator matrix?
$endgroup$
– Tahir Abbas
Mar 19 at 12:54
$begingroup$
Sorry, a typing error.
$endgroup$
– Wuestenfux
Mar 19 at 13:06
$begingroup$
would not it create a 3 x 7 generator matrix?
$endgroup$
– Tahir Abbas
Mar 19 at 12:54
$begingroup$
would not it create a 3 x 7 generator matrix?
$endgroup$
– Tahir Abbas
Mar 19 at 12:54
$begingroup$
Sorry, a typing error.
$endgroup$
– Wuestenfux
Mar 19 at 13:06
$begingroup$
Sorry, a typing error.
$endgroup$
– Wuestenfux
Mar 19 at 13:06
add a comment |
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