In
the last few decades, Lee-metric codes gained a lot of attention
especially with their promising application to code-based cryptography
as well as their connection to lattices. Even though, begin a rather old
metric considered in coding theory, there are still many open questions
regarding Lee metric codes regarding both the algebraic structure of
codes in the Lee metric as well as efficient decoding algorithms.
In this talk we present some selected topics on Lee-metric codes. We
start by introducing generalized Lee distances in order to derive
improved upper bounds on the minimum Lee distance. We discuss the
derivation of the bound as well as the density of codes achieving it. In
a next step we turn the attention to channel coding where we introduce
two channel models in the Lee metric. At this point we specifically
focus on a static channel model, introducing an error of fixed weight.
We derive its marginal distribution using typical sequences.
Additionally, this channel can be viewed as a design parameter to
code-based cryptography and hence, the knowledge of the marginal
distribution shows some implication in the field of cryptography too.
Lastly, we introduce classical random low-density parity-check (LDPC)
codes over a finite integer residue ring endowed with the Lee metric,
and we present their expected weight enumerator.