DocumentCode
1502236
Title
Optimal binary one-error-correcting codes of length 10 have 72 codewords
Author
Östergård, Patric R J ; Baicheva, Tsonka ; Kolev, Emil
Author_Institution
Dept. of Comput. Sci. & Eng., Helsinki Univ. of Technol., Espoo, Finland
Volume
45
Issue
4
fYear
1999
fDate
5/1/1999 12:00:00 AM
Firstpage
1229
Lastpage
1231
Abstract
The maximum number of codewords in a binary code with length n and minimum distance d is denoted by A(n, d). By construction it is known that A(10, 3)⩾72 and A(11, 3)⩾144. These bounds have long been conjectured to be the exact values. This is here proved by classifying various codes of smaller length and lengthening these using backtracking and isomorphism rejection. There are 562 inequivalent codes attaining A(10, 3)=72 and 7398 inequivalent codes attaining A(11, 3)=144
Keywords
backtracking; binary codes; error correction codes; optimisation; backtracking; bounds; code length; codewords; inequivalent codes; isomorphism rejection; minimum distance; optimal binary one-error-correcting codes; Binary codes; Computer science; Error correction codes; Hamming weight; Mathematics; Sections; Upper bound;
fLanguage
English
Journal_Title
Information Theory, IEEE Transactions on
Publisher
ieee
ISSN
0018-9448
Type
jour
DOI
10.1109/18.761273
Filename
761273
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