Bounds in the Lee Metric and Optimal Codes
Eimear Byrne, Violetta Weger
TL;DR
This paper explores bounds and optimal code structures in the Lee metric, introducing new bounds, characterizing optimal codes, and analyzing their density and properties.
Contribution
It presents a new Plotkin-like bound in the Lee metric, refines existing bounds, and characterizes Lee-equidistant codes, filling gaps in the current understanding.
Findings
New Plotkin-like bound outperforms previous bounds for non-free codes
Optimal Lee codes are very few and characterized in detail
Density of optimal codes with respect to the new bound is computed
Abstract
In this paper we investigate known Singleton-like bounds in the Lee metric and characterize optimal codes, which turn out to be very few. We then focus on Plotkin-like bounds in the Lee metric and present a new bound that extends and refines a previously known, and out-performs it in the case of non-free codes. We then compute the density of optimal codes with regard to the new bound. Finally we fill a gap in the characterization of Lee-equidistant codes.
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