New nonbinary code bounds based on divisibility arguments
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| Publication date | 2018 |
| Journal | Designs, Codes, and Cryptography |
| Volume | Issue number | 86 | 4 |
| Pages (from-to) | 861–874 |
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| Abstract | For q,n,d ∈ N, let Aq(n,d) be the maximum size of a code C⊆[q]n with minimum distance at least d. We give a divisibility argument resulting in the new upper bounds A5(8,6)≤65, A4(11,8)≤60 and A3(16,11)≤29. These in turn imply the new upper bounds A5(9,6)≤325, A5(10,6)≤1625, A5(11,6)≤8125 and A4(12,8)≤240. Furthermore, we prove that for μ,q∈N, there is a 1–1-correspondence between symmetric (μ,q)-nets (which are certain designs) and codes C⊆[q]μq of size μq2 with minimum distance at least μq−μ. We derive the new upper bounds A4(9,6)≤120 and A4(10,6)≤480 from these ‘symmetric net’ codes. |
| Document type | Article |
| Language | English |
| Published at | https://doi.org/10.1007/s10623-017-0366-0 |
| Other links | https://www.scopus.com/pages/publications/85019591993 |
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New nonbinary code
(Final published version)
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