Alternant code: Difference between revisions

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{{Short description|Class of error correction code}}

{{one source |date=April 2024}}

In [[coding theory]], '''alternant codes''' form a class of parameterised [[Error detection and correction|error-correcting codes]] which generalise the [[BCH code]]s.

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==Properties==

The parameters of this alternant code are length ''n'', dimension ≥ ''n'' − ''m''δ and minimum distance ≥ δ + 1.

There exist long alternant codes which meet the [[Gilbert-VarshamovGilbert–Varshamov bound]].

The class of alternant codes includes

* [[BCH code]]s

* [[Binary Goppa code|Goppa codes]]s

* [[Srivastava code]]s

== References ==

{{refbegin}}

* {{cite book | author=F.J. MacWilliams | authorlink=Jessie MacWilliams | coauthorsauthor2=N.J.A. Sloane | author2link=Neil 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/332 332–338] }}

{{refend}}

[[Category:Error detection and correction]]

[[Category:Finite fields]]

[[Category:Coding theory]]

{{crypto-stub}}