View source for Srivastava code

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A  class of parameterised [[error-correcting code]]s.  They are block  linear codes which are a special case of [[alternant code]]s.

The  original ''Srivastava code'' of length $n$ and parameter $s$ over  $GF(q)$ is defined by an $n \times s$ [[parity check matrix]] $H$ of  [[alternant matrix|alternant]] form 
$$
\begin{bmatrix}
\frac{\alpha_1^\mu}{\alpha_1-w_1} & \cdots & \frac{\alpha_n^\mu}{\alpha_n-w_1} \\ 
\vdots & \ddots & \vdots \\
\frac{\alpha_1^\mu}{\alpha_1-w_s} & \cdots & \frac{\alpha_n^\mu}{\alpha_n-w_s} \\ 
\end{bmatrix} 
$$
where the $\alpha_i$ and $z_i$ are elements of $GF(q^m)$.

The parameters of this code are length $n$, dimension $\ge n - ms$ and minimum distance $\ge s+1$.

== References ==
* F.J. MacWilliams. ''The  Theory of Error-Correcting Codes'' (North-Holland, 1977) ISBN 0-444-85193-3. pp.357-360