theprince94
New Member
I have a question in that coding, only to present it in y search and I didn't yet study that algorithme
If you have an idea, please try to help me
1)) One considers binary code BCH length 15, correct of 3 errors. The word received in the decoder is:
r(x) = x8 + x5 + x4 + x2 + x
What is the word of emitted code?
1) The whole of the zeros of the code is {1, 2,3,4,5,6}. Calculate the vector syndrome.
2) Define the fundamental system of decoding.
3) R (X) is affected of how many errors.
4) Calculate the polynomial locator.
5) By noticing that 1 is root of the polynomial locator, factorize the polynomial locator and determine the positions of the errors.
6) Find the word of emitted code.
2)) One considers the Reed-Solomon code length 15 defined by the generating polynomial:
g(x) = (x+1) (X + α)(X + α2)(X + α3)
The word received with the decoder is:
r(x) = α12x3 + α4x2 + x
1) Find the number, the positions and the values of the possible errors (it will be shown that 1 is root of the polynomial locator of errors).
2) By noting that any word of the code checks C, c.Ht = 0, give a matrix of parity of the code.
3) Calculations will be done in GF (16) defined by the primitive polynomial Ф (X) =x4+x+1, thanks to the following table:
the table I think that it's known of GF16
1+ α..... α 4
1+ α2.... α 8
1+ α3.... α 14
1+ α4.... α
1+ α5.... α10
1+ α6.... α13
1+ α7.... α9
1+ α8.... α2
1+ α9.... α7
1+ α10.... α 5
1+ α11.... α 12
1+ α12.... α 11
1+ α13.... α 6
1+ α14.... α 3
1 + 1 .... 0
1 + 0 .... 1
excuse me, the english is so bad because the question was written in French
But I think that you understand it
thank you advance
If you have an idea, please try to help me
1)) One considers binary code BCH length 15, correct of 3 errors. The word received in the decoder is:
r(x) = x8 + x5 + x4 + x2 + x
What is the word of emitted code?
1) The whole of the zeros of the code is {1, 2,3,4,5,6}. Calculate the vector syndrome.
2) Define the fundamental system of decoding.
3) R (X) is affected of how many errors.
4) Calculate the polynomial locator.
5) By noticing that 1 is root of the polynomial locator, factorize the polynomial locator and determine the positions of the errors.
6) Find the word of emitted code.
2)) One considers the Reed-Solomon code length 15 defined by the generating polynomial:
g(x) = (x+1) (X + α)(X + α2)(X + α3)
The word received with the decoder is:
r(x) = α12x3 + α4x2 + x
1) Find the number, the positions and the values of the possible errors (it will be shown that 1 is root of the polynomial locator of errors).
2) By noting that any word of the code checks C, c.Ht = 0, give a matrix of parity of the code.
3) Calculations will be done in GF (16) defined by the primitive polynomial Ф (X) =x4+x+1, thanks to the following table:
the table I think that it's known of GF16
1+ α..... α 4
1+ α2.... α 8
1+ α3.... α 14
1+ α4.... α
1+ α5.... α10
1+ α6.... α13
1+ α7.... α9
1+ α8.... α2
1+ α9.... α7
1+ α10.... α 5
1+ α11.... α 12
1+ α12.... α 11
1+ α13.... α 6
1+ α14.... α 3
1 + 1 .... 0
1 + 0 .... 1
excuse me, the english is so bad because the question was written in French
But I think that you understand it
thank you advance
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