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On Multifold MDS and Perfect Codes That Are Not Splittable into Onefold Codes

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Abstract

The union of ℓ disjoint MDS (or perfect) codes with distance 2 (respectively, 3) is always an ℓ-fold MDS (perfect) code. The converse is shown to be incorrect. Moreover, if k is a multiple of 4 and n + 1 ≥ 16 is a power of two, then a k/2-fold k-ary MDS code of length m ≥ 3 and an (n + 1)/8-fold perfect code of length n exist from which no MDS (perfect) code can be isolated.

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  1. Sobolev Institute of Mathematics, Siberian Branch of the RAS, Novosibirsk

    D. S. Krotov & V. N. Potapov

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  1. D. S. Krotov
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  2. V. N. Potapov
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Krotov, D.S., Potapov, V.N. On Multifold MDS and Perfect Codes That Are Not Splittable into Onefold Codes. Problems of Information Transmission 40, 5–12 (2004). https://doi.org/10.1023/B:PRIT.0000024875.79605.fc

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  • DOI: https://doi.org/10.1023/B:PRIT.0000024875.79605.fc

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