BCH code: Difference between revisions

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Revision as of 00:15, 27 November 2020

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One of the key features of BCH codes is that during code design, there is a precise control over the number of symbol errors correctable by the code. In particular, it is possible to design binary BCH codes that can correct multiple bit errors. Another advantage of BCH codes is the ease with which they can be decoded, namely, via an [[Abstract algebra|algebraic]] method known as [[syndrome decoding]]. This simplifies the design of the decoder for these codes, using small low-power electronic hardware.

BCH codes are used in applications such as satellite communications,<ref>{{cite web|title=Phobos Lander Coding System: Software and Analysis|url=http://ipnpr.jpl.nasa.gov/progress_report/42-94/94V.PDF|accessdateaccess-date=25 February 2012}}</ref> [[compact disc]] players, [[DVD]]s, [[Disk storage|disk drives]], [[solid-state drive]]s,<ref>{{cite web|title=Sandforce SF-2500/2600 Product Brief|url=http://www.sandforce.com/index.php?id=133&parentId=2&top=1|accessdateaccess-date=25 February 2012}}</ref> [[Post-quantum cryptography|quantum-resistant cryptography]]<ref>http://pqc-hqc.org/doc/hqc-specification_2020-05-29.pdf</ref> and [[Bar codes|two-dimensional bar codes]].

== Definition and illustration ==

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|author-link= Alexis Hocquenghem

|title=Codes correcteurs d'erreurs

|language= Frenchfr

|journal= Chiffres

|___location= Paris

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|pages= 147–156

|date= September 1959

}}

|issn=

|doi=}}

* {{Citation

|first= R. C.

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===Secondary sources===

* {{Citation|last=Gill |first=John |title=EE387 Notes #7, Handout #28 |date=n.d. |accessdateaccess-date=April 21, 2010 |pages=42–45 |publisher=Stanford University |url=http://www.stanford.edu/class/ee387/handouts/notes7.pdf |doi= }}{{dead link|date=July 2020|bot=medic}}{{cbignore|bot=medic}} Course notes are apparently being redone for 2012: http://www.stanford.edu/class/ee387/

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|first2= W. Wesley

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|last3= Zierler

|first3 = Neal

|authorlink3author-link3= Neal Zierler

|title= Two-Error Correcting Bose-Chaudhuri Codes are Quasi-Perfect

|journal= Information and Control

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|publisher= John Wiley

|year= 1999

}}

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|first2= Xuemin

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|year= 1999

|isbn= 0-7923-8528-4

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==Further reading==

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|publisher= John Wiley

|year= 2004

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|___location= Englewood Cliffs, NJ

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|first= F. J.

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|first2= N. J. A.

|last2= Sloane

|authorlink2author-link2= N. J. A. Sloane

|title= The Theory of Error-Correcting Codes

|___location= New York, NY

|publisher= North-Holland Publishing Company

|year= 1977

}}

|isbn=

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* {{Citation

|first = Atri

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|publisher = University at Buffalo

|url = http://www.cse.buffalo.edu/~atri/courses/coding-theory/

|accessdateaccess-date = April 21, 2010

|archive-url = https://web.archive.org/web/20100702120650/http://www.cse.buffalo.edu/~atri/courses/coding-theory/

|archive-date = 2010-07-02