Special sequences as subcodes of Reed–Solomon codes

We consider sequences in which every symbol of an alphabet occurs at most once. We construct families of such sequences as nonlinear subcodes of a $q$-ary $[n,k,n-k+1]_q$ Reed–Solomon code of length $n\le q$ consisting of words that have no identical symbols. We introduce the notion of a bunch of words of a linear code. For dimensions $k\le3$ we obtain constructive lower estimates (tight bounds in a number of cases) on the maximum cardinality of a subcode for various $n$ and $q$, and construct subsets of words meeting these estimates and bounds. We define codes with words that have no identical symbols, observe their relation to permutation codes, and state an optimization problem for them.