Abstract:
We propose new combinatorial constructions of partitions into perfect codes in
both the Hamming and Lee metrics. Also, we present a new combinatorial construction method
for diameter perfect codes in the Lee metric, which is further developed to a construction of
partitions into such codes. For the Lee metric, we improve previously known lower bounds on
the number of perfect and diameter perfect codes proposed by Etzion in 2011.
Keywords:perfect code, perfect code in the Hamming metric, perfect code in the Lee metric,
diameter perfect code in the Lee metric, partitions, partitions into perfect codes.
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