Srivastava 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

${\begin{bmatrix}{\frac {\alpha _{1}^{\mu }}{\alpha _{1}-w_{1}}}&\cdots &{\frac {\alpha _{n}^{\mu }}{\alpha _{n}-w_{1}}}\\\vdots &\ddots &\vdots \\{\frac {\alpha _{1}^{\mu }}{\alpha _{1}-w_{s}}}&\cdots &{\frac {\alpha _{n}^{\mu }}{\alpha _{n}-w_{s}}}\\\end{bmatrix}}$

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.

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.