please, the code BCH and RS a help

[theprince94]

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

 

[WTP Pepper]

I think there is a language barrier here, but stick with it....

The main idea behind error detection and correction is that you multiply your source signal with a polynomial at one end and divide by the same at the other end. If you get zero (the syndrome) then you have either no errors or are unlucky.

You can use a look up table to determine what syndrome gives bit errors in a certain position. You can XOR several bit errors to give multiple errors in different positions but when you get three bit errors you can run into problems as there is more than one solution that will give you the said syndrome.

I need more info to help you.