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| Authors | D.C. Gijswijt, A. Schrijver | | Title | New Upper Bounds for Nonbinary Codes Based on the Terwilliger Algebra and Semidefinite Programming |
| Journal | Journal of Combinatorial Theory, Series A |
| Volume | 113 |
| Year | 2006 |
| Issue | 8 |
| Pages | 1719-1731 |
| ISSN | 00973165 |
| Faculty | Faculty of Science |
| Institute/dept. | FNWI: Korteweg-de Vries Institute for Mathematics (KdVI) |
| 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 |
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