Abstract
In this paper we present a family of q-ary nonlinear quasi-perfect codes with covering radius 2. The codes have length \(n = q^m\) and size \( M = q^{n - m - 1}\) where q is a prime power, \(q \ge 3\), m is an integer, \(m \ge 2\). We prove that there are more than \(q^{q^{cn}}\) nonequivalent such codes of length n, for all sufficiently large n and a constant \(c = \frac{1}{q} - \varepsilon \).
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Communicated by T. Etzion.
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The work was carried out in the framework of the State Task to the Sobolev Institute of Mathematics (Project FWNF-2022-0018)
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Romanov, A.M. On the number of q-ary quasi-perfect codes with covering radius 2. Des. Codes Cryptogr. 90, 1713–1719 (2022). https://doi.org/10.1007/s10623-022-01070-y
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DOI: https://doi.org/10.1007/s10623-022-01070-y