An asymptotic property of quaternary additive codes
Document Type
Article
Publication Date
6-12-2024
Department
Department of Mathematical Sciences
Abstract
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).
Publication Title
Designs, Codes, and Cryptography
Recommended Citation
Bierbrauer, J.,
Marcugini, S.,
&
Pambianco, F.
(2024).
An asymptotic property of quaternary additive codes.
Designs, Codes, and Cryptography.
http://doi.org/10.1007/s10623-024-01438-2
Retrieved from: https://digitalcommons.mtu.edu/michigantech-p2/850