Journal of the
Korean Mathematical Society
JKMS
Article
ALL ARTICLES
View
J. Korean Math. Soc. 2007; 44(5): 1139-1162
Printed September 1, 2007
Copyright © The Korean Mathematical Society.
Optimal linear codes over $\mathbb{Z}_m$
Steven T. Dougherty, T. Aaron Gulliver, Young Ho Park, and John N. C. Wong
University of Scranton, University of Victoria, Kangwon National University, University of Victoria
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
MSC numbers: 94B05, 94B6
Article Tools
Stats or Metrics
Share this article on :
Related articles in JKMS
© 2022. The Korean Mathematical Society. Powered by INFOrang Co., Ltd