Please use this identifier to cite or link to this item:
https://open.uns.ac.rs/handle/123456789/6348
Title: | Perfect codes in the discrete simplex | Authors: | Kovačević, Marko Vukobratović, Dejan |
Issue Date: | 1-Jan-2015 | Journal: | Designs, Codes, and Cryptography | Abstract: | © 2013, Springer Science+Business Media New York. We study the problem of existence of (nontrivial) perfect codes in the discrete n-simplex Δnℓ ≔ {(x0,...,xn): xi ∈ ℤ+, ∑i xi = ℓ} under ℓ1 metric. The problem is motivated by the so-called multiset codes, which have recently been introduced by the authors as appropriate constructs for error correction in the permutation channels. It is shown that e-perfect codes in the 1-simplex Δ1ℓ exist for any ℓ ≥ 2e + 1, the 2-simplex Δ2ℓ admits an e-perfect code if and only if ℓ = 3e + 1, while there are no perfect codes in higher-dimensional simplices. In other words, perfect multiset codes exist only over binary and ternary alphabets. | URI: | https://open.uns.ac.rs/handle/123456789/6348 | ISSN: | 9251022 | DOI: | 10.1007/s10623-013-9893-5 |
Appears in Collections: | FTN Publikacije/Publications |
Show full item record
SCOPUSTM
Citations
13
checked on May 3, 2024
Page view(s)
26
Last Week
7
7
Last month
0
0
checked on May 10, 2024
Google ScholarTM
Check
Altmetric
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.