View source for Srivastava code

{{Short description|Class of error correction code}}
In [[Coding theory|coding theory]], '''Srivastava codes''', formulated by  Professor [[Biography:J. N. Srivastava|J. N. Srivastava]], form a class of parameterised [[Error detection and correction|error-correcting codes]] which are a special case of [[Alternant code|alternant code]]s. 

==Definition==
The original ''Srivastava code'' over GF(''q'') of length ''n'' is defined by a parity check matrix ''H'' of [[Alternant matrix|alternant]] form 

:<math>\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} 
</math>
where the α<sub>''i''</sub> and ''z''<sub>''i''</sub> are elements of GF(''q''<sup>''m''</sup>)

==Properties==
The parameters of this code are length ''n'', dimension ≥ ''n''&nbsp;&minus;&nbsp;''m''s and minimum distance ≥&nbsp;s&nbsp;+&nbsp;1.

== References ==
* {{cite book | author=F.J. 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]]



{{Sourceattribution|Srivastava code}}