(Perfect) Integer Codes Correcting Single Errors
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This letter presents a class of integer codes capable of correcting single errors. Unlike Hamming codes, the presented codes are constructed with the help of a computer. Among all codes of length up to 4096 bits, a computer search has found four perfect codes: (15, 10), (63, 56), (1023, 1012), and (4095, 4082). In addition, it is shown that, for practical data lengths up to 4096 bits, the proposed codes require only one check bit more compared to Hamming codes.
Keywords:
error correction / integer codes / perfect codes / single errorsSource:
IEEE Communications Letters, 2018, 22, 1, 17-20Publisher:
- IEEE
Note:
- This is the peer-reviewed version of the article: Radonjic, A., 2018. (Perfect) Integer Codes Correcting Single Errors. IEEE Communications Letters 22, 17–20. https://doi.org/10.1109/LCOMM.2017.2757465
DOI: 10.1109/LCOMM.2017.2757465
ISSN: 1089-7798
WoS: 000422706100004
Scopus: 2-s2.0-85031807207
Institution/Community
Институт техничких наука САНУ / Institute of Technical Sciences of SASATY - JOUR AU - Radonjić, Aleksandar PY - 2018 UR - https://dais.sanu.ac.rs/123456789/4638 AB - This letter presents a class of integer codes capable of correcting single errors. Unlike Hamming codes, the presented codes are constructed with the help of a computer. Among all codes of length up to 4096 bits, a computer search has found four perfect codes: (15, 10), (63, 56), (1023, 1012), and (4095, 4082). In addition, it is shown that, for practical data lengths up to 4096 bits, the proposed codes require only one check bit more compared to Hamming codes. PB - IEEE T2 - IEEE Communications Letters T1 - (Perfect) Integer Codes Correcting Single Errors SP - 17 EP - 20 VL - 22 IS - 1 DO - 10.1109/LCOMM.2017.2757465 UR - https://hdl.handle.net/21.15107/rcub_dais_4638 ER -
@article{ author = "Radonjić, Aleksandar", year = "2018", abstract = "This letter presents a class of integer codes capable of correcting single errors. Unlike Hamming codes, the presented codes are constructed with the help of a computer. Among all codes of length up to 4096 bits, a computer search has found four perfect codes: (15, 10), (63, 56), (1023, 1012), and (4095, 4082). In addition, it is shown that, for practical data lengths up to 4096 bits, the proposed codes require only one check bit more compared to Hamming codes.", publisher = "IEEE", journal = "IEEE Communications Letters", title = "(Perfect) Integer Codes Correcting Single Errors", pages = "17-20", volume = "22", number = "1", doi = "10.1109/LCOMM.2017.2757465", url = "https://hdl.handle.net/21.15107/rcub_dais_4638" }
Radonjić, A.. (2018). (Perfect) Integer Codes Correcting Single Errors. in IEEE Communications Letters IEEE., 22(1), 17-20. https://doi.org/10.1109/LCOMM.2017.2757465 https://hdl.handle.net/21.15107/rcub_dais_4638
Radonjić A. (Perfect) Integer Codes Correcting Single Errors. in IEEE Communications Letters. 2018;22(1):17-20. doi:10.1109/LCOMM.2017.2757465 https://hdl.handle.net/21.15107/rcub_dais_4638 .
Radonjić, Aleksandar, "(Perfect) Integer Codes Correcting Single Errors" in IEEE Communications Letters, 22, no. 1 (2018):17-20, https://doi.org/10.1109/LCOMM.2017.2757465 ., https://hdl.handle.net/21.15107/rcub_dais_4638 .