[For the entire collection see Zbl 0561.00003.]
The survey treats three different combinatorial problems, all concerned with the ternary alphabet \(A=\{0,1,*\}\). A code C of length n is a subset of \(A^ n\). The distance d(\b{x},\b{y}) of two elements of C is the number of places where one has a 0, the other a 1, i.e. * does not contribute to distance.
In the addressing problem for graphs the vertices of a connected graph G are given addresses from a code C, such that the distance of the addresses equals the distance of the vertices in G. N(G) is the minimal value of n for which this is possible. The recent proof by P. Winkler [Combinatorica 3, 135-139 (1983; Zbl 0522.05064)] that N(G)\(\leq | G| -1\) is described and the generalization to directed graphs is discussed.
An associative block design ABD(k,w) is a code C of cardinality \(b=2^ w\) in \(A^ k\) such that each word has k-w stars, the code array has a constant number of stars per column, and any two distinct words have distance at least 1. A survey of what is known about such designs is given.
A tournament code also has the property that different words have positive distance and furthermore if \(a_ i=0\), \(b_ i=1\) then there is no index j such that \(a_ j=1\), \(b_ j=0\). The problem which is discussed is studying the function \[ t(k):=\{\max | C| /\quad C\quad is\quad tournament\quad code\quad of\quad length\quad k\}. \] The most interesting result is the inequality \(t(n^ 2+n+1)\geq n(n^ 2+n+1)+2\) proved by K. Collins, P. Shor, and J. Stembridge.