1 research outputs found
Perfect Codes in the Discrete Simplex
We study the problem of existence of (nontrivial) perfect codes in the
discrete -simplex under metric. The problem is motivated by the so-called multiset
codes, which have recently been introduced by the authors as appropriate
constructs for error correction in the permutation channels. It is shown that -perfect codes in the -simplex exist for any , the -simplex admits an -perfect
code if and only if , while there are no perfect codes in
higher-dimensional simplices. In other words, perfect multiset codes exist only
over binary and ternary alphabets.Comment: 15 pages (single-column), 5 figures. Minor revisions made. Accepted
for publication in Designs, Codes and Cryptograph