Srivastava code

{{Short description|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.

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 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.

References

  • {{cite book | author=F.J. MacWilliams | authorlink=Jessie MacWilliams |author2=N.J.A. Sloane | title=The Theory of Error-Correcting Codes | url=https://archive.org/details/theoryoferrorcor0000macw | url-access=registration | publisher=North-Holland | date=1977 | isbn=0-444-85193-3 | pages=[https://archive.org/details/theoryoferrorcor0000macw/page/357 357–360] }}

Category:Error detection and correction

Category:Finite fields

Category:Coding theory

{{crypto-stub}}