Srivastava code
From HandWiki
Short description: Class of error correction 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
- [math]\displaystyle{ \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} }[/math]
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
- F.J. MacWilliams; N.J.A. Sloane (1977). The Theory of Error-Correcting Codes. North-Holland. pp. 357–360. ISBN 0-444-85193-3. https://archive.org/details/theoryoferrorcor0000macw.
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