Reed-Solomon codes were introduced by Reed and Solomon in the 1960s. These codes are still used in storage device, from compact-disc player to deep-space application. And they are widely used mainly because of two features: first of all, because they are MDS code, that is, they attain the maximum error detection and correction capacity. The second thing is that they have efficient decoding algorithms. Reed-Solomon codes are particularly useful for burst error correction, that is, they are effective for channels that have memory.So, suppose that we consider n and k nonnegative integers such that they verify this inequality. Now, we take an n-tuple a of elements from the field that are all different. And we take an n-tuple b of elements from the field which are non-zero.The polynomial vector space of all polynomials that have d