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Optimal additive quaternary codes of low dimension
[article]
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
arXiv:2007.05482v1
fatcat:wso7phaaivdnfp4ufbengspihq