Srivastava code

Srivastava code

In coding theory, Srivastava codes 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

:egin{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" − "m"s and minimum distance ≥ s + 1.

References

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