Design of Reed-Solomon Code where $n < q-1$

1. How is Reed-Solomon calculated?
2. How do Reed-Solomon codes work?
3. What is RS in code?
4. How many errors can Reed-Solomon correct?

How is Reed-Solomon calculated?

A Reed-Solomon codeword has 2t syndromes that depend only on errors (not on the transmitted code word). The syndromes can be calculated by substituting the 2t roots of the generator polynomial g(x) into r(x). This can be done using the Berlekamp-Massey algorithm or Euclid's algorithm.

How do Reed-Solomon codes work?

Reed–Solomon codes are able to detect and correct multiple symbol errors. By adding t = n − k check symbols to the data, a Reed–Solomon code can detect (but not correct) any combination of up to t erroneous symbols, or locate and correct up to ⌊t/2⌋ erroneous symbols at unknown locations.

What is RS in code?

Reed-Solomon (RS) codes are an important subclass of non-binary BCH codes. RS codes have a true minimum distance which is the maximum possible for a linear (n, k) code, as in Equation 14.27. They are therefore examples of maximum-distance-separable codes.

How many errors can Reed-Solomon correct?

The standard (255, 223) Reed-Solomon code is capable of correcting up to 16 Reed-Solomon symbol errors in each codeword. Since each symbol is actually eight bits, this means that the code can correct up to 16 short bursts of error due to the inner convolutional decoder.