Optimal Additive Quaternary Codes of Low Dimension

An additive quaternary [n,k,d]-code (length n, dimension k, minimum distance d) is a 2k-dimensional \mathbb F 2 -vector space of n-tuples with entries in ⊕\mathbb (the 2-dimensional vector over ) Hamming d. We determine the optimal parameters codes k ≤ 3. The most challenging case k=2.5. prove that an [n,2.5,d]-code where d <; n-1 exists if and only 3(n-d) ≥ d/2+d/4+d/8 articular, we construct new 2.5-dimensional codes. As by-product, give direct proof for fact binary linear [3m,5,2e] -code e m-1 Griesmer bound 3(m-e) e/2+e/4+e/8 satisfied.