  Local rank modulation scheme was suggested recently for representing
information in flash memories in order to overcome drawbacks of rank
modulation. For $s\leq t\leq n$ with $s|n$, $(s,t,n)$-LRM scheme is a local
rank modulation scheme where the $n$ cells are locally viewed through a sliding
window of size $t$ resulting in a sequence of small permutations which requires
less comparisons and less distinct values. The distance between two windows
equals to $s$. To get the simplest hardware implementation the case of sliding
window of size two was presented. Gray codes and constant weight Gray codes
were presented in order to exploit the full representational power of the
scheme. In this work, a tight upper-bound for cyclic constant weight Gray code
in $(1,2,n)$-LRM scheme where the weight equals to $2$ is given. Encoding,
decoding and enumeration of $(1,3,n)$-LRM scheme is studied.
