OPTIMAL LINEAR CODES OVER ℤm
Steven T. Dougherty, Thomas Aaron Gulliver, Young-Ho Park, John N. C. Wong · Journal of the Korean Mathematical Society · 2007
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.