New bounds for \(n_{4}(k,d)\) and classification of some optimal codes over GF(4)
The authors study the problem of determining the value of \(n_4(k,d)\) -- the shortest possible length of a quaternary code of fixed dimension \(k\) and fixed minimum distance \(d\). For values of \(k\) smaller than 5, this problem has been solved for all \(d\). For 5-dimensional codes there were some 200 undecided values for \(d\). The authors provide lots of constructions thus finding many exact values or improving bounds on \(n_4(5,d)\). They leave 132 undecided values of \(d\) for which \(n_4(5,d)\) is still unknown. The paper contains also an enumeration for some short optimal quaternary codes of dimension \(k=3,4,5,6\).
scientific article; zbMATH DE number 2083658