Srivastava code
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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.
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 α i and z i are elements of GF(q m )
Properties
The parameters of this code are length n, dimension ≥ n − ms and minimum distance ≥ s + 1.
Related constructions
The symmetry properties of Srivastava-code parity-check matrices have been used to construct binary codes, including a construction that generalizes Goppa's construction.
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