An asymptotic property of quaternary additive codes

Abstract: Let $n_k(s)$ be the maximal length $n$ such that a quaternary additive $[n,k,n-s]_4$-code exists. We solve a natural asymptotic problem by determining the lim sup $\lambda_k$ of $n_k(s)/s,$ and the smallest value of $s$ such that $n_k(s)/s=\lambda_k.$ Our new family of quaternary additive codes has parameters $$[4^{k-1,k,4^{k-4^{{k-1}]_4=[2^{{2k}-1,k,3\cdot}}}} 2<sup>{2k-2}]_4$$ (where $k=l/2$ and $l$ is an odd integer). These are constant-weight codes. The binary codes obtained by concatenation meet the Griesmer bound with equality. The proof is in terms of multisets of lines in $PG(l-1,2).$