Tactical decompositions of designs over finite fields

An automorphism group of an incidence structure I induces a tactical decomposition on I . It is well known that tactical decompositions of t -designs satisfy certain necessary conditions which can be expressed as equations in terms of the coefficients of tactical decomposition matrices. In this arti...

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Bibliographic Details
Published in:Designs, codes, and cryptography codes, and cryptography, 2015-10, Vol.77 (1), p.49-60
Main Authors: Nakić, Anamari, Pavčević, Mario Osvin
Format: Article
Language:English
Subjects:
Circuits
Coding and Information Theory
Computer Science
Cryptology
Data Structures and Information Theory
Discrete Mathematics in Computer Science
Information and Communication
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Summary:An automorphism group of an incidence structure I induces a tactical decomposition on I . It is well known that tactical decompositions of t -designs satisfy certain necessary conditions which can be expressed as equations in terms of the coefficients of tactical decomposition matrices. In this article we present results obtained for tactical decompositions of q -analogs of t -designs, more precisely, of 2 - ( v , k , λ 2 ; q ) designs. We show that coefficients of tactical decomposition matrices of a design over finite field satisfy an equation system analog to the one known for block designs. Furthermore, taking into consideration specific properties of designs over the binary field F 2 , we obtain an additional system of inequations for these coefficients in that case.
ISSN:0925-1022
1573-7586
DOI:10.1007/s10623-014-9988-7