(Perfect) Integer Codes Correcting Single Errors

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 (...

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Bibliographic Details
Published in:IEEE communications letters 2018-01, Vol.22 (1), p.17-20
Main Author: Radonjic, Aleksandar
Format: Article
Language:English
Subjects:
Decoding
Encoding
Error correction
Error correction codes
Indexes
Integer codes
perfect codes
Physical layer
Redundancy
single errors
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Summary: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.
ISSN:1089-7798
1558-2558
DOI:10.1109/LCOMM.2017.2757465