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Paper 2022/296

On new results on Extremal Graph Theory, Theory of Algebraic Graphs and their applications in Cryptography and Coding Theory.

Vasyl Ustimenko

Abstract

New explicit constructions of infinite families of finite small world graphs of large girth with well defined projective limits which is an infinite tree are described. The applications of these objects to constructions of LDPC codes and cryptographic algorithms are shortly observed. We define families of homogeneous algebraic graphs of large girth over commutative ring K. For each commutative integrity ring K with |K|>2 we introduce a family of bipartite homogeneous algebraic graphs of large girth over K formed by graphs with sets of points and lines isomorphic K^n, n>1 and cycle indicator ≥ 2n+2 such that their projective limit is well defined and isomorphic to an infinite forest.

Metadata
Available format(s)
PDF
Category
Foundations
Publication info
Published elsewhere. Minor revision. will be published in Dopovidi of Nath. Acad. of Ukraine
Keywords
family of graphs of large girthsmall world graphscryptographic algorithmsLDPC codes.
Contact author(s)
vasyl @ hektor umcs lublin pl
History
2022-03-07: received
Short URL
https://ia.cr/2022/296
License
Creative Commons Attribution
CC BY
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