New Upper Bounds for Nonbinary Codes Based on the Terwilliger Algebra and Semidefinite Programming
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| Publication date | 2006 |
| Journal | Journal of Combinatorial Theory. Series A |
| Volume | Issue number | 113 | 8 |
| Pages (from-to) | 1719-1731 |
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| Abstract |
Abstract: We give a new upper bound on the maximum size $A_q(n,d)$ of a code of word length $n$ and minimum Hamming distance at least $d$ over the alphabet of $q\geq 3$ letters. By block-diagonalizing the Terwilliger algebra of the nonbinary Hamming scheme, the bound can be calculated in time polynomial in $n$ using semidefinite programming. For $q=3,4,5$ this gives several improved upper bounds for concrete values of $n$ and $d$. This work is related to \cite{Lex}, where a similar approach is used to derive upper bounds for binary codes. |
| Document type | Article |
| Published at | https://doi.org/10.1016/j.jcta.2006.03.010 |
| Published at | http://www.sciencedirect.com/science/journal/00973165 |
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