Abstract
A <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">q</tex> -nary error-correcting code with <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N = q^{k}</tex> code words of length <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n = k + r</tex> can have no greater minimum distance <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</tex> than <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r+1</tex> . The class of codes for which <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d = r+1</tex> is studied first in general, then with the restriction that the codes be linear. Examples and construction methods are given to show that these codes exist for a number of values of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">q, k</tex> , and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</tex> .
Keywords
Code (set theory)Computer scienceAlgorithmProgramming language
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Publication Info
- Year
- 1964
- Type
- article
- Volume
- 10
- Issue
- 2
- Pages
- 116-118
- Citations
- 508
- Access
- Closed
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Cite This
R. C. Singleton
(1964).
Maximum distanceq-nary codes.
IEEE Transactions on Information Theory
, 10
(2)
, 116-118.
https://doi.org/10.1109/tit.1964.1053661
Identifiers
- DOI
- 10.1109/tit.1964.1053661