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arXiv · 1509.05348

Quasi-perfect codes in the $\ell_p$ metric

João E. Strapasson·Grasiele C. Jorge·Antonio Campello·Sueli I. R. Costa
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Abstract

We consider quasi-perfect codes in $\mathbb{Z}^n$ over the $\ell_p$ metric, $2 \leq p < \infty$. Through a computational approach, we determine all radii for which there are linear quasi-perfect codes for $p = 2$ and $n = 2, 3$. Moreover, we study codes with a certain \textit{degree of imperfection}, a notion that generalizes the quasi-perfect codes. Numerical results concerning the codes with the smallest degree of imperfection are presented.

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João E. Strapasson, Grasiele C. Jorge, Antonio Campello, Sueli I. R. Costa. 2015-09-17. Quasi-perfect codes in the $\ell_p$ metric. https://arxiv.org/abs/1509.05348

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