Generalized Reed-Solomon code
= Generalized Reed-Solomon code
{title2=$\operatorname{GRS}_k(a,v)$}
= GRS code
{c}
{synonym}
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 $\deg f<k$. It remains a <maximum distance separable code>. Its <dual code> is another generalized Reed-Solomon code with dimension $n-k$ and multipliers proportional to $v_i^{-1}\prod_{j\ne i}(a_i-a_j)^{-1}$.