Bounds on packings and coverings by spheres in \(q\)-ary and mixed Hamming spaces (Q1176382)

The paper discusses bounds on sphere packings and sphere coverings in \(q\)-ary or mixed (binary/ternary) Hamming spaces \(H\). For given integers \(e\) and \(R\), let \(N\) be the maximum cardinality \(| C|\) of a code \(C\) in \(H\) with packing radius \(e\), and \(K\) the minimum cardinality \(| C|\) of a code \(C\) in \(H\) with covering radius \(R\). Extending earlier work on lower bounds on \(K\) for binary covering codes [the author, IEEE Trans. Inf. Theory IT-34, No. 2, 237-245 (1988; Zbl 0653.94014)], lower bounds are now proved for the nonbinary case. Also, similar techniques are used to find upper bounds on \(N\) for the packing problem.