22 research outputs found
An Algorithm for constructing Hjelmslev planes
Projective Hjelmslev planes and Affine Hjelmselv planes are generalisations
of projective planes and affine planes. We present an algorithm for
constructing a projective Hjelmslev planes and affine Hjelsmelv planes using
projective planes, affine planes and orthogonal arrays. We show that all
2-uniform projective Hjelmslev planes, and all 2-uniform affine Hjelsmelv
planes can be constructed in this way. As a corollary it is shown that all
2-uniform Affine Hjelmselv planes are sub-geometries of 2-uniform projective
Hjelmselv planes.Comment: 15 pages. Algebraic Design Theory and Hadamard matrices, 2014,
Springer Proceedings in Mathematics & Statistics 13
Repairable Block Failure Resilient Codes
In large scale distributed storage systems (DSS) deployed in cloud computing,
correlated failures resulting in simultaneous failure (or, unavailability) of
blocks of nodes are common. In such scenarios, the stored data or a content of
a failed node can only be reconstructed from the available live nodes belonging
to available blocks. To analyze the resilience of the system against such block
failures, this work introduces the framework of Block Failure Resilient (BFR)
codes, wherein the data (e.g., file in DSS) can be decoded by reading out from
a same number of codeword symbols (nodes) from each available blocks of the
underlying codeword. Further, repairable BFR codes are introduced, wherein any
codeword symbol in a failed block can be repaired by contacting to remaining
blocks in the system. Motivated from regenerating codes, file size bounds for
repairable BFR codes are derived, trade-off between per node storage and repair
bandwidth is analyzed, and BFR-MSR and BFR-MBR points are derived. Explicit
codes achieving these two operating points for a wide set of parameters are
constructed by utilizing combinatorial designs, wherein the codewords of the
underlying outer codes are distributed to BFR codeword symbols according to
projective planes
Finite complexes with infinitely-generated groups of self-equivalences
Aprovat pel Ple del CESB de 3-12-201