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http://dx.doi.org/10.4134/JKMS.2007.44.5.1139

OPTIMAL LINEAR CODES OVER ℤm  

Dougherty, Steven T. (Department of Mathematics University of Scranton)
Gulliver, T. Aaron (Department of Electrical and Computer Engineering University of Victoria)
Park, Young-Ho (Department of Mathematics Kangwon National University)
Wong, John N.C. (Department of Electrical and Computer Engineering University of Victoria)
Publication Information
Journal of the Korean Mathematical Society / v.44, no.5, 2007 , pp. 1139-1162 More about this Journal
Abstract
We examine the main linear coding theory problem and study the structure of optimal linear codes over the ring ${\mathbb{Z}}_m$. We derive bounds on the maximum Hamming weight of these codes. We give bounds on the best linear codes over ${\mathbb{Z}}_8$ and ${\mathbb{Z}}_9$ of lengths up to 6. We determine the minimum distances of optimal linear codes over ${\mathbb{Z}}_4$ for lengths up to 7. Some examples of optimal codes are given.
Keywords
linear codes; optimal codes; codes over rings;
Citations & Related Records

Times Cited By Web Of Science : 4  (Related Records In Web of Science)
Times Cited By SCOPUS : 3
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