×

zbMATH — the first resource for mathematics

On partitions of \(q\)-ary Hamming codes into disjoint components. (Russian) Zbl 1078.94035
The method of \(i\)-components for the \(q\)-ary Hamming code is investigated. Certain necessary and sufficient conditions for disjointness of such components are given. Special regular partitions of the \(q\)-ary Hamming code into \(i\)-components are presented by induction. Some lower bound on the number of different nonlinear \(q\)-ary perfect codes is claimed to yield from the construction.
{Later this bound was improved by A. V. Los’ in [Construction of perfect \(q\)-ary codes by switchings of simple components. Proc. Int. Workshop on Optimal Codes, Pamporovo, Bulgaria, June 2005, 226–231 (2005)].}

MSC:
94B25 Combinatorial codes
94B65 Bounds on codes
PDF BibTeX XML Cite