… 2 shows a representation of the Lipschitz graph generated … In order to define codes over the
Lipschitz integers, we adopt the … of perfect codes over Lipschitz integers by considering the …

… Now, we will look for perfect dominating sets over Lipschitz graphs. Solving this problem …
of perfect codes over integer quaternions. The concepts of domination and perfect dominating …

… schemes are possible over Abelian Cayley graphs using perfect codes in for example …
schemes from perfect codes in Cayley graphs over Gaussian integers [6] and Lipschitz integers [7]…

… a result of the authors in an earlier work, Perfect Mannheim, Lipschitz and Hurwitz weight
codes, … We illustrate the construction described in the proof above in the next example. …

… Constacyclic codes over Lipschitz integers The purpose of this section is to define constacyclic
codes over H(Z)π obtained from Lipschitz integers. The definitions of these codes depend …

… perfect codes for the two-dimensional Lee spaces and perfect codes over Gaussian integers
… paper with the quasi-perfect Lee codes is also investigated. It will be shown that new quasi-…

… new perfect 1-errorcorrecting codes we obtain in the present study, there are perfect codes
… Following the standard terminology, see [3], we thus say that π is a prime Lipschitz integer if …

… In [16–20], works on codes over Lipschitz or Hurwitz integers were given. … In this section,
we obtain perfect codes correcting errors of the Hurwitz weight one over Жπ. Recall that, the …

… Abstract—Codes over quotient rings of Lipschitz integers … of Lipschitz integer constellations
for transmission over the AWGN … A construction of sets of Lipschitz integers is presented that …

… study perfect codes and total perfect codes in Cayley graphs, with a focus on the following
themes: when a subgroup of a given group is a (total) perfect code … for any fixed integer n ≥ 1 …