OPTIMAL LINEAR CODES OVER ℤm Dougherty, Steven T.; Gulliver, T. Aaron; Park, Young-Ho; Wong, John N.C.;
We examine the main linear coding theory problem and study the structure of optimal linear codes over the ring . We derive bounds on the maximum Hamming weight of these codes. We give bounds on the best linear codes over and of lengths up to 6. We determine the minimum distances of optimal linear codes over for lengths up to 7. Some examples of optimal codes are given.