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Srivastava code

From Encyclopedia of Mathematics
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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 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
How to Cite This Entry:
Srivastava code. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Srivastava_code&oldid=54440