Naslov
Equations of tactical decomposition of designs: application to the problem of existence of 3- (16, 7, 5) design

Autori
Nakić, Anamari

Vrsta, podvrsta i kategorija rada
Sažeci sa skupova, kratko priopćenje, znanstveni

Izvornik
Combinatorics 2014, Gaeta, Italija, 1–6.06.2014. / - , 2014, 1-1

Skup
Combinatorics 2014

Mjesto i datum
Gaeta, Italija, 01.06.2014. - 06.06.2014

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
design over finite field ; q-analog of design ; automorphism group ; tactical decomposition
(combinatorial design ; automorphism group ; tactical decomposition)

Sažetak
We address tactical decomposition of t- (v, k, lambda_t) designs. Equations for coefficients of tactical decomposition matrices when t=2 are well-known. In this talk, we generalize these equations and propose an explicit equation system for coefficients of tactical decomposition matrices for t- (v, k, lambda_t) designs, for any integer value of t. This system of equations for coefficients of tactical decomposition matrices represents necessary conditions for the existence of t- designs with an assumed automorphism group. The problem of existence of a 3-(16, 7, 5) design is one of the open problems in design theory. These parameters describe one of the smallest 3- designs for which the question of existence is still unsolved. Previous results show that if a 3- (16, 7, 5) design admits an automorphism of a prime order $p$, then p = 2, 3. We use equations of tactical decomposition to eliminate the case p = 3.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA