Srivastava code explained

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} (\alpha ^{\mu} _{1})/(\alpha _{1-w} _{1}) & … & (\alpha ^{\mu} _{n})/(\alpha _{n-w} _{1}) \ \vdots & \ddots & \vdots \\ (\alpha ^{\mu} _{1})/(\alpha _{1-w} _{s}) & … & (\alpha ^{\mu} _{n})/(\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.

References

• Book: Jessie MacWilliams

. F.J. MacWilliams . Jessie MacWilliams . N.J.A. Sloane . The Theory of Error-Correcting Codes . registration . North-Holland . 1977 . 0-444-85193-3 . 357–360 .