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This paper 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.

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This page is a summary of: (Perfect) Integer Codes Correcting Single Errors, IEEE Communications Letters, January 2017, Institute of Electrical & Electronics Engineers (IEEE), DOI: 10.1109/lcomm.2017.2757465.
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