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2019-04-01T04:04:23Z

Created page with "In coding theory, '''alternant codes''' form a class of parameterised error-correcting codes which generalise the BCH codes. ==Defi..."

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

==Definition==
An ''alternant code'' over GF(''q'') of length ''n'' is defined by a [[parity]] check matrix ''H'' of alternant form ''H''''i'',''j'' = αji''y''''i'', where the α''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 δ − 1, ''j'' from 1 to ''n''.

==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-Varshamov bound.

The class of alternant codes includes
* [[BCH code]]s
* [[Goppa code]]s
* [[Srivastava code]]s

==Source==

[http://wikipedia.org/ http://wikipedia.org/]
[[Category:Error-correcting codes]]
==See Also on BitcoinWiki==
* [[TrustedCars]]
* [[Mainframe]]
* [[NIST5]]
* [[Exit Address]]
* [[BL3P]]

Alternant code - Revision history

Admin: Created page with "In coding theory, '''alternant codes''' form a class of parameterised error-correcting codes which generalise the BCH codes. ==Defi..."