BCH code: Difference between revisions

Revision as of 22:03, 7 August 2023

Revision as of 21:34, 22 September 2023

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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 |archive-url=https://ghostarchive.org/archive/20221009/http://ipnpr.jpl.nasa.gov/progress_report/42-94/94V.PDF |archive-date=2022-10-09 |url-status=live|access-date=25 February 2012}}</ref> [[compact disc]] players, [[DVD]]s, [[Disk storage|disk drives]], [[USB flash drive]]s, [[solid-state drive]]s,<ref>{{cite web|title=SandforceBCH SF-2500/2600Codes Productfor BriefSolid-State-Drives|url=httphttps://wwwlink.sandforcespringer.com/indexchapter/10.php?id=133&parentId=2&top=11007/978-981-13-0599-3_11|access-date=2523 FebruarySeptember 20122023}}</ref> [[Post-quantum cryptography|quantum-resistant cryptography]]<ref>http://pqc-hqc.org/doc/hqc-specification_2020-05-29.pdf {{Bare URL PDF|date=March 2022}}</ref> and [[Bar codes|two-dimensional bar codes]].

== Definition and illustration ==