Srivastava code

The original Srivastava code over GF(q) of length n is defined by a parity check matrix H of alternant form

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

where the α_i and z_i are elements of GF(q^m)

The parameters of this code are length n, dimension ≥ n − ms and minimum distance ≥ s + 1.

The symmetry properties of Srivastava-code parity-check matrices have been used to construct binary codes, including a construction that generalizes Goppa's construction.^[1]