Srivastava code (original) (raw)

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Class of error correction 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.

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}}} {\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 − _m_s and minimum distance ≥ s + 1.