On lattice tilings of $\mathbb{Z}^{n}$ by limited magnitude error balls $\mathcal{B}(n,2,1,1)$

TL;DR

This paper classifies all lattice tilings of integer lattices by specific limited magnitude error balls, which are relevant for error correction in flash memory systems.

Contribution

It provides a complete classification of lattice tilings of ^n by (n,2,1,1), advancing understanding of error correction codes in memory devices.

Findings

Complete classification of lattice tilings by (n,2,1,1)

Connections between tilings and perfect codes in flash memory

Implications for designing error correction schemes

Abstract

Limited magnitude error model has applications in flash memory. In this model, a perfect code is equivalent to a tiling of $\mathbb{Z}^n$ by limited magnitude error balls. In this paper, we give a complete classification of lattice tilings of $\mathbb{Z}^n$ by limited magnitude error balls $\mathcal{B}(n,2,1,1)$.