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
[ α 1 μ α 1 − w 1 ⋯ α n μ α n − w 1 ⋮ ⋱ ⋮ α 1 μ α 1 − w s ⋯ α n μ α n − w s ] {\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}}}
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.
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.