 Generalized Reed-Solomon code

ID: generalized-reed-solomon-code

A generalized Reed-Solomon code consists of

(v_{i} f (a_{i}))_{i = 1}^{n}

, where the evaluation points are distinct, all coordinate multipliers

v_{i}

are nonzero, and

de g f < k

. It remains a maximum distance separable code. Its dual code is another generalized Reed-Solomon code with dimension

n - k

and multipliers proportional to

v_{i}^{- 1} \prod_{j \neq = i} (a_{i} - a_{j})^{- 1}

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