Lower bounds on the minimum distance of long codes in the Lee metric (Q2256106)

The minimum distance of codes over various alphabets and the Lee metric are here studied via generalizations of bounds for the Hamming metric. A seminal study of such generalizations was carried out by \textit{J. Astola} [Discrete Appl. Math. 8, 13--23 (1984; Zbl 0538.94019)], who considered the Hamming and Gilbert-Varshamov bounds. The focus here is on a generalization of a lower bound in the Hamming metric due to Tsfasman, Vlădut and Zink [\textit{M. A. Tsfasman} et al., Math. Nachr. 109, 21--28 (1982; Zbl 0574.94013)]. The results obtained are constructive, whereas the Hamming and Gilbert-Varshamov bounds obtained by Astola and others are non-constructive. In particular, the current paper utilizes algebraic-geometric codes due to Wu, Kuijper and Udaya [\textit{X.-W. Wu} et al., Electron. Lett. 43, 820--821 (2007)]. Asymptotic results for the various types of bounds are compared.