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A class of parameterised [[error-correcting code]]s which generalise the [[BCH code]]s.

An  ''alternant code'' over $GF(q)$ of length $n$ is defined by a parity  check matrix $H$ of [[alternant matrix|alternant]] form $H_{i,j} =  \alpha_j^i y_i$, where the $\alpha_j$ are distinct elements of the  extension $GF(q^m)$, the $y_i$ are further non-zero parameters again in  the extension $GF(q^m)$ and the indices range as $i$ from 0 to  $\delta-1$, $j$ from 1 to $n$.

The parameters of this alternant code are length $n$, dimension $\ge n - m\delta$ and minimum distance $\ge \delta+1$.  There exist long alternant codes which meet the [[Gilbert-Varshamov bound]].

The class of alternant codes includes [[BCH code]]s, [[Goppa code]]s and [[Srivastava code]]s.

== References ==
* F.J. MacWilliams, N.J.A. Sloane. ''The Theory of Error-Correcting Codes'' (North-Holland, 1977) {{ISBN|0-444-85193-3}}, pp.332-338