19,245 research outputs found
Generalized packing designs
Generalized -designs, which form a common generalization of objects such
as -designs, resolvable designs and orthogonal arrays, were defined by
Cameron [P.J. Cameron, A generalisation of -designs, \emph{Discrete Math.}\
{\bf 309} (2009), 4835--4842]. In this paper, we define a related class of
combinatorial designs which simultaneously generalize packing designs and
packing arrays. We describe the sometimes surprising connections which these
generalized designs have with various known classes of combinatorial designs,
including Howell designs, partial Latin squares and several classes of triple
systems, and also concepts such as resolvability and block colouring of
ordinary designs and packings, and orthogonal resolutions and colourings.
Moreover, we derive bounds on the size of a generalized packing design and
construct optimal generalized packings in certain cases. In particular, we
provide methods for constructing maximum generalized packings with and
block size or 4.Comment: 38 pages, 2 figures, 5 tables, 2 appendices. Presented at 23rd
British Combinatorial Conference, July 201
Jacobi polynomials and design theory II
In this paper, we introduce some new polynomials associated to linear codes
over . In particular, we introduce the notion of split complete
Jacobi polynomials attached to multiple sets of coordinate places of a linear
code over , and give the MacWilliams type identity for it. We
also give the notion of generalized -colored -designs. As an application
of the generalized -colored -designs, we derive a formula that obtains
the split complete Jacobi polynomials of a linear code over
.Moreover, we define the concept of colored packing (resp.
covering) designs. Finally, we give some coding theoretical applications of the
colored designs for Type~III and Type~IV codes.Comment: 28 page
Generalized PSK in Space Time Coding
A wireless communication system using multiple antennas promises reliable
transmission under Rayleigh flat fading assumptions. Design criteria and
practical schemes have been presented for both coherent and non-coherent
communication channels. In this paper we generalize one dimensional phase shift
keying (PSK) signals and introduce space time constellations from generalized
phase shift keying (GPSK) signals based on the complex and real orthogonal
designs. The resulting space time constellations reallocate the energy for each
transmitting antenna and feature good diversity products, consequently their
performances are better than some of the existing comparable codes. Moreover
since the maximum likelihood (ML) decoding of our proposed codes can be
decomposed to one dimensional PSK signal demodulation, the ML decoding of our
codes can be implemented in a very efficient way.Comment: 22 pages, 3 figures, submitted to IEEE transactions on communicaton
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