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.
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
TY - 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 .
