Srivastava code

In coding theory, Srivastava codes, formulated by Professor J. N. Srivastava, 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  ms and minimum distance ≥ s + 1.

References


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