BCH code: Difference between revisions

Revision as of 21:34, 22 September 2023

Revision as of 13:02, 13 December 2023

Line 4:

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 webbook|titlechapter=BCH Codes for Solid-State-Drives|doi=10.1007/978-981-13-0599-3_11 |chapter-url=https://link.springer.com/chapter/10.1007/978-981-13-0599-3_11|access-date=23 September 2023 |title=Inside Solid State Drives (SSDS) |series=Springer Series in Advanced Microelectronics |date=2018 |last1=Marelli |first1=Alessia |last2=Micheloni |first2=Rino |volume=37 |pages=369–406 |isbn=978-981-13-0598-6 }}</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 ==

Line 621:

}}

* {{Citation

|firstfirst1= R. C.

|lastlast1= Bose

|author-link= R. C. Bose

|first2= D. K.

Line 640:

* {{Citation|last=Gill |first=John |title=EE387 Notes #7, Handout #28 |date=n.d. |access-date=April 21, 2010 |pages=42–45 |publisher=Stanford University |url=http://www.stanford.edu/class/ee387/handouts/notes7.pdf |archive-url=https://ghostarchive.org/archive/20221009/http://www.stanford.edu/class/ee387/handouts/notes7.pdf |archive-date=2022-10-09 |url-status=live }}{{dead link|date=June 2021|bot=medic}}{{cbignore|bot=medic}} Course notes are apparently being redone for 2012: http://www.stanford.edu/class/ee387/ {{Webarchive|url=https://web.archive.org/web/20130605170343/http://www.stanford.edu/class/ee387/ |date=2013-06-05 }}

* {{Citation

|lastlast1= Gorenstein

|firstfirst1= Daniel

|author-link= Daniel Gorenstein

|last2= Peterson

Line 658:

}}

* {{Citation

|firstfirst1= Rudolf

|lastlast1= Lidl

|first2= Günter

|last2= Pilz

Line 668:

}}

* {{Citation

|firstfirst1= Irving S.

|lastlast1= Reed

|author-link= Irving S. Reed

|first2= Xuemin

Line 683:

* {{Citation |last1=Blahut |first1=Richard E. |author-link1=Richard Blahut |title=Algebraic Codes for Data Transmission |edition=2nd |publisher=[[Cambridge University Press]] |year=2003 |isbn=0-521-55374-1}}

* {{Citation

|firstfirst1= W. J.

|lastlast1= Gilbert

|first2= W. K.

|last2= Nicholson

Line 693:

}}

* {{Citation

|firstfirst1= S.

|lastlast1= Lin

|first2= D.

|last2= Costello

Line 703:

}}

* {{Citation

|firstfirst1= F. J.

|lastlast1=MacWilliams

|first2= N. J. A.

|last2= Sloane