Semidefinite code bounds based on quadruple distances

Let $A(n,d)$ be the maximum number of $0,1$ words of length $n$, any two having Hamming distance at least $d$. We prove $A(20,8)=256$, which implies that the quadruply shortened Golay code is optimal. Moreover, we show $A(18,6)\leq 673$, $A(19,6)\leq 1237$, $A(20,6)\leq 2279$, $A(23,6)\leq 13674$, $A(19,8)\leq 135$, $A(25,8)\leq 5421$, $A(26,8)\leq 9275$, $A(21,10)\leq 47$, $A(22,10)\leq 84$, $A(24,10)\leq 268$, $A(25,10)\leq 466$, $A(26,10)\leq 836$, $A(27,10)\leq 1585$, $A(25,12)\leq 55$, and $A(26,12)\leq 96$. The method is based on the positive semidefiniteness of matrices derived from quadruples of words. This can be put as constraint in a semidefinite program, whose optimum value is an upper bound for $A(n,d)$. The order of the matrices involved is huge. However, the semidefinite program is highly symmetric, by which its feasible region can be restricted to the algebra of matrices invariant under this symmetry. By block diagonalizing this algebra, the order of the matrices will be reduced so as to make the program solvable with semidefinite programming software in the above range of values of $n$ and $d$.Comment: 15 page

Avaliação da reação de resistência à ferrugem da folha e do colmo à campo no germoplasma de azevém da Embrapa, safra 2006.

bitstream/CNPGL/12932/1/comunicado_167.pd

Avaliação da reação de resistência à ferrugem da folha e do colmo à campo no germoplasma de azevém da Embrapa, safra 2006.

bitstream/item/31297/1/comunicado-167.pd

Doenças do azevém.

bitstream/CNPGL-2010/17105/1/documento-279.pd

Doenças do azevém.

bitstream/CPACT-2010/13088/1/documento-279.pd

Situação atual e demandas de pesquisa, desenvolvimento e inovação tecnológica em forrageiras e pastagens - Região Sul do Rio Grande do Sul.

bitstream/item/33620/1/documento-178.pd

Use of Patterns for Knowledge Management in the Ceramic Tile Design Chain

Knowledge Management (KM) is a complex objective, especially in the instance of extended enterprises consisting of SMEs, and critical in new product design and development (NPD). The use of patterns is essential to get KM in collaborative NPD processes. This paper presents the use of patterns adopted in the CE-TILE project to standardize information and knowledge in collaborative work. The different types of patterns and models established for the knowledge capture, formalization and configuration are also described