Optimal additive quaternary codes of low dimension [article]

Juergen Bierbrauer, Stefano Marcugini, Fernanda Pambianco
2020 arXiv   pre-print
An additive quaternary [n,k,d]-code (length n, quaternary dimension k, minimum distance d) is a 2k-dimensional F_2-vector space of n-tuples with entries in Z_2× Z_2 (the 2-dimensional vector space over F_2) with minimum Hamming distance d. We determine the optimal parameters of additive quaternary codes of dimension k≤ 3. The most challenging case is dimension k=2.5. We prove that an additive quaternary [n,2.5,d]-code where d<n-1 exists if and only if 3(n-d)≥ d/2 + d/4 + d/8. In particular we
more » ... nstruct new optimal 2.5-dimensional additive quaternary codes. As a by-product we give a direct proof for the fact that a binary linear [3m,5,2e]_2-code for e<m-1 exists if and only if the Griesmer bound 3(m-e)≥ e/2 + e/4+ e/8 is satisfied.
arXiv:2007.05482v1 fatcat:wso7phaaivdnfp4ufbengspihq