Algebraic decoding of the binary systematic (71, 36, 11) quadratic residue code

A fast and efficient algebraic decoding algorithm (ADA) is proposed to correct up to five possible error patterns in the binary systematic (71, 36, 11) quadratic residue (QR) code. The technique required here is based on the ADA developed by He et al. [2001. Decoding the (47, 24, 11) quadratic resid...

Full description

Saved in:
Bibliographic Details
Published in:Journal of the Chinese Institute of Engineers Vol. 36; no. 3; pp. 399 - 404
Main Authors: Lee, Hung-Peng, Chang, Hsin-Chiu, Chu, Shao-I
Format: Journal Article
Language:English
Published: Taylor & Francis Group 01.04.2013
Subjects:
algebraic decoding algorithm
quadratic residue code
syndrome
ISSN:0253-3839, 2158-7299
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Abstract A fast and efficient algebraic decoding algorithm (ADA) is proposed to correct up to five possible error patterns in the binary systematic (71, 36, 11) quadratic residue (QR) code. The technique required here is based on the ADA developed by He et al. [2001. Decoding the (47, 24, 11) quadratic residue code. IEEE transactions on information theory, 47 (3), 1181-1186.] and the modification of the ADA developed by Lin et al. [2010. Decoding of the (31, 16, 7) quadratic residue code. Journal of the Chinese institute of engineers, 33 (4), 573-580; 2010. High speed decoding of the binary (47, 24, 11) quadratic residue code. Information sciences, 180 (20), 4060-4068]. The new proposed conditions and the error-locator polynomials for different numbers of errors in the received word are derived. Simulation results show that the decoding speed of the proposed ADA is faster than the other existing ADAs.
AbstractList A fast and efficient algebraic decoding algorithm (ADA) is proposed to correct up to five possible error patterns in the binary systematic (71, 36, 11) quadratic residue (QR) code. The technique required here is based on the ADA developed by He et al. [2001. Decoding the (47, 24, 11) quadratic residue code. IEEE transactions on information theory, 47 (3), 1181-1186.] and the modification of the ADA developed by Lin et al. [2010. Decoding of the (31, 16, 7) quadratic residue code. Journal of the Chinese institute of engineers, 33 (4), 573-580; 2010. High speed decoding of the binary (47, 24, 11) quadratic residue code. Information sciences, 180 (20), 4060-4068]. The new proposed conditions and the error-locator polynomials for different numbers of errors in the received word are derived. Simulation results show that the decoding speed of the proposed ADA is faster than the other existing ADAs.
Author Lee, Hung-Peng
Chang, Hsin-Chiu
Chu, Shao-I
Author_xml – sequence: 1
  givenname: Hung-Peng
  surname: Lee
  fullname: Lee, Hung-Peng
  email: hpl@center.fotech.edu.tw
  organization: Department of Computer Science and Information Engineering , Fortune Institute of Technology
– sequence: 2
  givenname: Hsin-Chiu
  surname: Chang
  fullname: Chang, Hsin-Chiu
  organization: Department of Communication Engineering , Xiamen University
– sequence: 3
  givenname: Shao-I
  surname: Chu
  fullname: Chu, Shao-I
  organization: Department of Electrical Engineering , I-Shou University
BookMark eNqFkL1OwzAUhS1UJNrCGzB4BIkU_8ROzIKqij-pEgMwW7ZjF6M0BjsV6sbKa_IkJAQWBlju1dU95-jebwJGTWgsAIcYzTAq0SkijNKSihlBmMwK2s1iB4wJZmVWECFGYNxLsl6zByYpPSFEOCN4DO7m9crqqLyBlTWh8s0KBgfbRwu1b1TcwrRNrV2rtlMcFfjk4-2d8r5ifAxfNqqKX6tok682FnYRdh_sOlUne_Ddp-Dh8uJ-cZ0tb69uFvNlZigq2izXTjNEOcl5aSrHMTelKLgwmFlKHNd5yTRzQivHrMWal0hxhR3VgubUCjoF-ZBrYkgpWiefo193N0uMZA9G_oCRPRg5gOlsZ79sxrfdE6FpOw71f-bzwewbF-JavYZYV7JV2zpEF1VjfJL0z4RPmTJ9-g
CitedBy_id crossref_primary_10_1080_02533839_2012_742704
crossref_primary_10_1049_iet_com_2015_0159
crossref_primary_10_1109_TCOMM_2015_2481894
Cites_doi 10.1109/TC.1985.1676616
10.1109/18.915677
10.1016/j.ins.2009.06.002
10.1109/TIT.1964.1053699
10.1109/TCOMM.2003.816994
10.1016/j.ins.2010.06.022
10.1080/02533839.2010.9671645
ContentType Journal Article
Copyright Copyright Taylor & Francis Group, LLC 2013
Copyright_xml – notice: Copyright Taylor & Francis Group, LLC 2013
DBID AAYXX
CITATION
DOI 10.1080/02533839.2012.730259
DatabaseName CrossRef
DatabaseTitle CrossRef
DatabaseTitleList
DeliveryMethod fulltext_linktorsrc
Discipline Engineering
EISSN 2158-7299
EndPage 404
ExternalDocumentID 10_1080_02533839_2012_730259
730259
GroupedDBID -~X
.7F
.QJ
0BK
0R~
30N
4.4
5GY
AAENE
AAGDL
AAHIA
AAJMT
AALDU
AAMIU
AAPUL
AAQRR
ABCCY
ABFIM
ABLIJ
ABPAQ
ABPEM
ABTAI
ABXUL
ABXYU
ACGFS
ACTIO
ADCVX
ADGTB
AEISY
AENEX
AEOZL
AFRVT
AGDLA
AGMYJ
AHDZW
AIJEM
AIYEW
AKBVH
AKOOK
ALMA_UNASSIGNED_HOLDINGS
ALQZU
AQRUH
AQTUD
AVBZW
BLEHA
CCCUG
DGEBU
DKSSO
EBS
EJD
E~A
E~B
FRP
GTTXZ
H13
HF~
HZ~
H~P
J.P
KYCEM
M4Z
NA5
NX~
O9-
RIG
RNANH
ROSJB
RTWRZ
S-T
SNACF
TASJS
TBQAZ
TDBHL
TEN
TFL
TFT
TFW
TTHFI
TUROJ
UT5
UU3
ZGOLN
~S~
07I
8RM
AAYXX
ACTTO
ADMLS
ADUMR
ADXEU
AEHZU
AEZBV
AFBWG
AFION
AGBKS
AGVKY
AGWUF
AGYFW
AKHJE
AKMBP
ALRRR
ALXIB
BGSSV
BWMZZ
C0-
CITATION
CYRSC
DAOYK
DEXXA
FETWF
IFELN
LJTGL
OPCYK
TAJZE
UB6
ID FETCH-LOGICAL-c307t-4bfb50362468cdf616c89769c15e32f6b485b5f9baf5ee1b680a6a1f3b9343e93
IEDL.DBID TFW
ISICitedReferencesCount 3
ISICitedReferencesURI http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000318160600011&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
ISSN 0253-3839
IngestDate Sat Nov 29 05:10:24 EST 2025
Tue Nov 18 22:29:39 EST 2025
Mon Oct 20 23:45:03 EDT 2025
IsPeerReviewed true
IsScholarly true
Issue 3
Language English
LinkModel DirectLink
MergedId FETCHMERGED-LOGICAL-c307t-4bfb50362468cdf616c89769c15e32f6b485b5f9baf5ee1b680a6a1f3b9343e93
PageCount 6
ParticipantIDs crossref_citationtrail_10_1080_02533839_2012_730259
informaworld_taylorfrancis_310_1080_02533839_2012_730259
crossref_primary_10_1080_02533839_2012_730259
PublicationCentury 2000
PublicationDate 4/1/2013
PublicationDateYYYYMMDD 2013-04-01
PublicationDate_xml – month: 04
  year: 2013
  text: 4/1/2013
  day: 01
PublicationDecade 2010
PublicationTitle Journal of the Chinese Institute of Engineers
PublicationYear 2013
Publisher Taylor & Francis Group
Publisher_xml – name: Taylor & Francis Group
References CIT0001
CIT0003
CIT0002
CIT0005
CIT0004
Prange E (CIT0008) 1957
CIT0006
MacWilliams FJ (CIT0007) 1977
CIT0009
References_xml – ident: CIT0009
  doi: 10.1109/TC.1985.1676616
– ident: CIT0003
  doi: 10.1109/18.915677
– ident: CIT0004
  doi: 10.1016/j.ins.2009.06.002
– volume-title: The theory of error correcting codes
  year: 1977
  ident: CIT0007
– ident: CIT0002
  doi: 10.1109/TIT.1964.1053699
– ident: CIT0001
  doi: 10.1109/TCOMM.2003.816994
– ident: CIT0006
  doi: 10.1016/j.ins.2010.06.022
– volume-title: Cyclic error-correcting codes in two symbols
  year: 1957
  ident: CIT0008
– ident: CIT0005
  doi: 10.1080/02533839.2010.9671645
SSID ssj0026521
ssj0001654702
Score 1.9063444
Snippet A fast and efficient algebraic decoding algorithm (ADA) is proposed to correct up to five possible error patterns in the binary systematic (71, 36, 11)...
SourceID crossref
informaworld
SourceType Enrichment Source
Index Database
Publisher
StartPage 399
SubjectTerms algebraic decoding algorithm
quadratic residue code
syndrome
Title Algebraic decoding of the binary systematic (71, 36, 11) quadratic residue code
URI https://www.tandfonline.com/doi/abs/10.1080/02533839.2012.730259
Volume 36
WOSCitedRecordID wos000318160600011&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
hasFullText 1
inHoldings 1
isFullTextHit
isPrint
journalDatabaseRights – providerCode: PRVAWR
  databaseName: Taylor and Francis Online Journals
  customDbUrl:
  eissn: 2158-7299
  dateEnd: 99991231
  omitProxy: false
  ssIdentifier: ssj0026521
  issn: 0253-3839
  databaseCode: TFW
  dateStart: 19780101
  isFulltext: true
  titleUrlDefault: https://www.tandfonline.com
  providerName: Taylor & Francis
link http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV07T8MwELZQxQADb0R5yQMDSBjq2HGcsUJUTBUSRXSLbMdGlaoW2pSZlb_JL8GXR5sOgARLlsSn6OLzfef4-w6hM8t0KmLNibWcEW6CiMTchEQHKRVKS92yKm82EXW7st-P72ssfjhWCTW0K4Qi8rUaglvpaXUi7tqnaSisgGZCgys_RT2E94uwz_wQmb3O02KTBVrrtuZ6UoEIcyIWGCBgoeLSfWN0KVctKZnWclBn8_9vv4U2SvyJ28WE2UYrdrSD1muqhLvooT18ht_JA4NTX5xCcsNjhz1SxDpn7-KF_DM-j-jl5_sHE3Cl9AK_zlQ6yW_5Qn6QziwG1vweeuzc9m7uSNl7gRgf9Rnh2ukQshsX0qROUGGkRy6xoaFlgROay1CHLtbKhdZSLWRLCUUd0zHjzMZsHzVG45E9QJh7xEAjZTwS0h7-pVIDPUj5yklRUNtvIlZ5OTGlMDn0xxgmtNIvLV2WgMuSwmVNROajXgphjl-el_UPmGT5hogrupck7Kehh38feoTWgrx_Bhz1OUaNbDKzJ2jVvGWD6eQ0n6xfzczh2w
linkProvider Taylor & Francis
linkToHtml http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwrV07T8MwELagIAEDb0R5emAACUMdO04yVoiqiFIhUUS3yHZsVKlqoQ9mVv4mvwRfkr4GQEIsWZI7RZdz7jv77juETgxTiYgUJ8ZwRrj2AhJx7RPlJVRIFaqSkemwiaBeD5vN6D6vJuznZZWQQ9uMKCL9V8Pihs3oUUncpYvTkFlBnwn1LpyPOgw_jxZ8F2qBPr9ReZpss8Bw3dKYUcoTftqKBRoIqBh1032jdSZazXCZTkWhyto_vP86Ws0hKC5nPrOB5kxnE61MERNuoYdy-xlOlFsaJy4_hfiGuxY7sIhV2sCLJwzQ-DSg55_vH0zAldIz_DqUSS-95XL5VjI0GBrnt9Fj5bpxVSX5-AWi3cIfEK6s8iHAcRHqxAoqdOjAS6Spb5hnheKhr3wbKWl9Y6gSYUkKSS1TEePMRGwHFTrdjtlFmDvQQAOpHRhSDgEmoYIOIemSJ0mBcL-I2MjMsc65yWFERjumIwrT3GQxmCzOTFZEZCz1knFz_PJ8OP0F40G6J2KzASYx-0l07--ix2ip2rirxbWb-u0-WvbScRpQ-XOACoPe0ByiRf02aPV7R6nnfgE38uYF
linkToPdf http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV07T8MwELagIAQDb0R5emAACUMdO04yVkAFAlWVKKJbZDs2qlS1pbTMrPxNfgm-PNoyABIsWRJb0eWc-86-7zuEjgxTiYgUJ8ZwRrj2AhJx7RPlJVRIFaqKkWmziaBeD1utqDHF4oeySsihbSYUkf6rYXH3E1tUxJ27MA2JFdBMqHfmXNRB-Fk055CzAB9v1h4nuyzQW7cyFpTyhJ8ysWAGAlMUZLpvZv0SrL5ImU4FodrK_19_FS3nABRXM49ZQzOmu46WpmQJN9B9tfME58ltjROXnUJ0wz2LHVTEKqXv4on-Mz4O6OnH2zsTcKX0BD-PZDJIb7lMvp2MDAba_CZ6qF01L65J3nyBaLfsh4Qrq3wIb1yEOrGCCh066BJp6hvmWaF46CvfRkpa3xiqRFiRQlLLVMQ4MxHbQqVur2u2EeYOMtBAageFlMN_SaiAHyRd6iQpyO2XESusHOtcmRwaZHRiWgiY5iaLwWRxZrIyIuNR_UyZ45fnw-kPGA_THRGbtS-J2U9Dd_4-9BAtNC5r8d1N_XYXLXppLw0o-9lDpeFgZPbRvH4dtl8GB6nffgKJfeS3
openUrl ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Algebraic+decoding+of+the+binary+systematic+%2871%2C%E2%80%8936%2C%E2%80%8911%29+quadratic+residue+code&rft.jtitle=Journal+of+the+Chinese+Institute+of+Engineers&rft.au=Lee%2C+Hung-Peng&rft.au=Chang%2C+Hsin-Chiu&rft.au=Chu%2C+Shao-I&rft.date=2013-04-01&rft.pub=Taylor+%26+Francis+Group&rft.issn=0253-3839&rft.eissn=2158-7299&rft.volume=36&rft.issue=3&rft.spage=399&rft.epage=404&rft_id=info:doi/10.1080%2F02533839.2012.730259&rft.externalDocID=730259
thumbnail_l http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0253-3839&client=summon
thumbnail_m http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0253-3839&client=summon
thumbnail_s http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0253-3839&client=summon