Proof of the minimum distance of Reed-Solomon codes

1. What is the minimum distance of a RS code?
2. Are Reed-Solomon codes MDS?
3. What is the distance of T error correcting Reed-Solomon code?
4. How many bits can Reed-Solomon correct?

What is the minimum distance of a RS code?

Since the minimum distance of BCH codes is 2t + 1, the minimum distance of RS codes is d_min= n − k + 1, therefore satisfying the Singleton bound (d_min ≤ n − k + 1) with equality and belonging to the class of maximum-distance separable (MDS) codes.

Are Reed-Solomon codes MDS?

Codes which achieve this bound, i.e for which n = k+d−1, are called MDS codes (Maximal Distance Separable). What we just showed is that Reed-Solomon codes are MDS codes.

What is the distance of T error correcting Reed-Solomon code?

In Reed-Solomon codes, message size is given by (n-2t) where t= number of errors corrected. Parity check size is given by = (n-k) or 2t symbols. Minimum distance(a) is given by = (2t+1). Message size is of k bits.

How many bits 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.