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 λ_k of n_k (s)/s for s going to infinity, and the smallest value of s such that n_k (s)/s = λ_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 · 2^2k−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).
An asymptotic property of quaternary additive codes
· Stefano Marcugini;· Fernanda Pambianco
2024
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 λ_k of n_k (s)/s for s going to infinity, and the smallest value of s such that n_k (s)/s = λ_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 · 2^2k−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).File in questo prodotto:
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