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On multifold MDS and perfect codes that are not splittable into onefold codes. (English. Russian original) Zbl 1083.94022
Probl. Inf. Transm. 40, No. 1, 5-12 (2004); translation from Probl. Peredachi Inf. 40, No. 1, 6-14 (2004).
Summary: The union of \(\ell\) disjoint MDS (or perfect) codes with distance 2 (respectively, 3) is always an \(\ell\)-fold MDS (perfect) code. The converse is shown to be incorrect. Moreover, if \(k\) is a multiple of 4 and \(n+1\geq 16\) is a power of two, then a \(k/2\)-fold \(k\)-ary MDS code of length \(m\geq 3\) and an \((n+1)/8\)-fold perfect code of length \(n\) exist from which no MDS (perfect) code can be isolated.

MSC:
94B65 Bounds on codes
94B99 Theory of error-correcting codes and error-detecting codes
05B15 Orthogonal arrays, Latin squares, Room squares
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