Alternant code: Difference between revisions

Revision as of 04:03, 23 July 2008

Latest revision as of 03:29, 28 April 2024

(14 intermediate revisions by 13 users not shown)

Line 1:

{{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.

Line 5 ⟶ 7:

==Properties==

The parameters of this alternant code are length ''n'', dimension ≥ ''n-mδ'' − ''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

* [[SrivastaSrivastava 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/332-338 332–338] }}

{{refend}}

[[Category:Error detection and correction]]

Line 20 ⟶ 24:

[[Category:Coding theory]]

{{algebracrypto-stub}}