17,161 research outputs found
Recursive Methods for Construction of Balanced N-ary Block Designs
2000 Mathematics Subject Classification: Primary 05B05; secondary 62K10.This paper presents a recursive method for the construction of
balanced n-ary block designs.
This method is based on the analogy between a balanced incomplete
binary block design (B.I .E .B) and the set of all distinct linear sub-varieties of
the same dimension extracted from a finite projective geometry. If V1
is the
first B.I .E .B resulting from this projective geometry, then by regarding any
block of V1 as a projective geometry, we obtain another system of B.I .E .B.
Then, by reproducing this operation a finite number of times, we get a
family of blocks made up of all obtained B.I .E .B blocks. The family being
partially ordered, we can obtain an n-ary design in which the blocks are
consisted by the juxtaposition of all binary blocks completely nested. These
n-ary designs are balanced and have well defined parameters. Moreover, a
particular balanced n-ary class is deduced with an appreciable reduction of
the number of blocks
Constructions of balanced ternary designs based on generalized Bhaskar Rao designs
New series of balanced ternary designs and partially balanced ternary designs are obtained. Some of the designs in the series are non-isomorphic solutions for design parameters which were previously known or whose solution was obtained by trial and error, rather than by a systematic method
Secondary constructions of (non)weakly regular plateaued functions over finite fields
Plateaued (vectorial) functions over finite fields have diverse applications in symmetric cryptography, coding theory, and sequence theory. Constructing these functions is an attractive research topic in the literature. We can distinguish two kinds of constructions of plateaued functions: secondary constructions and primary constructions. The first method uses already known functions to obtain new functions while the latter do not need to use previously constructed functions to obtain new functions. In this work, the first secondary constructions of (non)weakly regular plateaued (vectorial) functions are presented over the finite fields of odd characteristics. We also introduce some recursive constructions of (non)weakly regular plateaued p-ary functions by using already known such functions. We obtain nontrivial plateaued functions from the previously known trivial plateaued (partially bent) functions in the proposed construction methods
Coding Theory and Algebraic Combinatorics
This chapter introduces and elaborates on the fruitful interplay of coding
theory and algebraic combinatorics, with most of the focus on the interaction
of codes with combinatorial designs, finite geometries, simple groups, sphere
packings, kissing numbers, lattices, and association schemes. In particular,
special interest is devoted to the relationship between codes and combinatorial
designs. We describe and recapitulate important results in the development of
the state of the art. In addition, we give illustrative examples and
constructions, and highlight recent advances. Finally, we provide a collection
of significant open problems and challenges concerning future research.Comment: 33 pages; handbook chapter, to appear in: "Selected Topics in
Information and Coding Theory", ed. by I. Woungang et al., World Scientific,
Singapore, 201
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