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.
TY - JOUR
AU - Radonjić, Aleksandar
PY - 2018
UR - http://dais.sanu.ac.rs/123456789/3753
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
ER -
@article{
author = "Radonjić, Aleksandar",
year = "2018",
url = "http://dais.sanu.ac.rs/123456789/3753",
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"
}
Radonjić A. (Perfect) Integer Codes Correcting Single Errors. IEEE Communications Letters. 2018;22(1):17-20
,& Radonjić, A. (2018). (Perfect) Integer Codes Correcting Single Errors.
IEEE Communications LettersIEEE., 22(1), 17-20.
https://doi.org/10.1109/LCOMM.2017.2757465
