With RS codes, you should be able to detect (n-k) errors and correct up to (n-k)/2 errors. What kind of algorithm are you using in your code, is it the Berlekamp-Massey algorithm? In Berlekamp-Massey, you construct an error-locator polynomial to detect the location of the errors, then with a seperate error-magnitude polynomial, you find the magnitude of these errors. With this two information you can correct (n-k)/2 errors. Since the detection capability is (n-k), I suppose error-locator polynomial finds (n-k) errors. Probably, you should concentrate on the information provided by this polynomial.
If you are using any other algorithm (Peterson-Gorenstein-Zierler or Euclidean), I suggest you to refer to the books "Error Control Systems for Digital Communication and Storage" by Wicker and "Error Control Coding" by Lin and Costello. These are great sources also for the Berlekamp-Massey algorithm.
Serhann,
I have tried using the Euclidean algorithm. Since RS(15,13) code has only 2 syndromes, my syndrome equation would be S1(x) + S0
Using further equations i finally got an the error locator polynomial which is of degree 1.(From R&D white paper WHP031 , published 2002)
This means i would find only one error location which is the root of the equation.
Can u please try explaining me how to detect the second error
I am yet to design the code completely. Im still working on it.
Presently, I can get an error location with s0 + ~s1
and error value as s0
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https://downloads.bbc.co.uk/rd/pubs/whp/whp-pdf-files/WHP031.pdf
Here is the paper i am currenly referring to.
The paper has an example which i am currenly looking into.
The example is showed for RS(15,11). which means we can detect upto 4 errors and correct 2 errors.
So according to the example, the error locator polynomial is of degree 2 so, the number of error locations he can get is 2.
In order to find 4 error locations, we need a polynomial of degree 4?? is this right??
If yes, how do we get the 4 degree polynomial