An asymptotic property of quaternary additive codes

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Let nk(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 λk of nk(s)/s for s going to infinity, and the smallest value of s such that nk(s)/s=λk. Our new family of quaternary additive codes has parameters [4k-1,k,4k-4k-1]4=[22k-1,k,3·22k-2]4 (where k=l/2 and l is an odd integer). These are constant-weight codes. The binary codes obtained by concatenation with inner code [3,2,2]2 meet the Griesmer bound with equality. The proof is in terms of multisets of lines in PG(l-1,2).

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Designs, Codes, and Cryptography