Tables for Constant Composition Codes

Abstract

A constant composition code of length $n$ over a $k$-ary alphabet has the property that the numbers of occurrences of the $k$ symbols within a codeword is the same for each codeword. These specialize to constant weight codes in the binary case, and permutation codes in the case that each symbol occurs exactly once. Constant composition codes arise in powerline communication and balanced scheduling, and are used in the construction of permutation codes. Using exhaustive and probabilistic clique search, and by applying theorems and constructions in past literature, we generate tables which summarize the best known lower bounds on constant composition codes for (i) $3\le k\le 8$, (ii) $k=3$, $9\le n\le 12$, and (iii) various other interesting parameters with $n\ge 9$.