linguistic:paraphrasing
Constructions (encoding)

The Reed–Solomon code is actually a family of codes, where every code is characterised by three parameters: an alphabet size q {\displaystyle q}, a block length n {\displaystyle n}, and a message length k {\displaystyle k}, with k < n ≤ q {\displaystyle k<n\leq q}. The set of alphabet symbols is interpreted as the finite field F {\displaystyle F} of order q {\displaystyle q}, and thus, q {\displaystyle q} must be a prime power. In the most useful parameterizations of the Reed–Solomon code, the block length is usually some constant multiple of the message length, that is, the rate R = k n {\displaystyle R={\frac {k}{n}}} is some constant, and furthermore, the block length is equal to or one less than the alphabet size, that is, n = q {\displaystyle n=q} or n = q − 1 {\displaystyle n=q-1}.