Srivastava code

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

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 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