Srivastava code

In coding theory, Srivastava codes form a class of parameterised error-correcting codes which are a special case of alternant codes.

Definition
The original Srivastava code over GF(q) of length n is defined by a parity check matrix H of 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 αi and zi are elements of GF(qm)

Properties
The parameters of this code are length n, dimension ≥ n &minus; ms and minimum distance ≥ s + 1.