Naslov
Self-orthogonal or self-dual codes from orbit matrices of block designs

Autori
Crnković, Dean

Vrsta, podvrsta i kategorija rada
Sažeci sa skupova, neobjavljeni rad, znanstveni

Skup
Mathematics of Communications: Sequences, Codes and Designs

Mjesto i datum
Banff, Kanada, 25.01.2015. - 30.01.2015

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
self-orthogonal code ; self-dual code, block design, orbit matrix

Sažetak
In [1] Harada and Tonchev have introduced a construction of self-orthogonal codes from orbit matrices of symmetric designs with fixed-point-free automorphisms. As a generalization of that result, a construction of self-orthogonal codes from orbit matrices of block designs admitting certain automorphisms with fixed points (and blocks) is desribed in [3]. Using this result, classes of self-orthogonal or self-dual codes from orbit matrices of certain Menon designs have been constructed in [2]. In [4] Lander proved that rows of extended incidence matrices of symmetric designs under some conditions span self-dual codes. Further, a chain of codes is used for a construction of a self-dual code from an extended incidence matrix of a symmetric (v, k, lambda) design, when a prime p divides n* (a square-free part of n), where n is the order of a symmetric design. We show that under some conditions these results can be extended to orbit matrices of symmetric designs. References [1] M. Harada, V. D. Tonchev, Self-orthogonal codes from symmetric designs with fixed-point-free automorphisms, Discrete Math. 264 (2003), 81–90. [2] D. Crnkovi´c, Classes of self-orthogonal or self-dual codes from orbit matrices of Menon designs, Discrete Math. 327 (2014), 91-95. [3] D. Crnkovi´c, B. G. Rodrigues, S. Rukavina, L. Simˇci´c, Self-orthogonal codes from orbit matrices of 2-designs, Adv. Math. Commun. 7 (2013), 161–174. [4] E. Lander, Symmetric Designs: An Algebraic Approach, Cambridge University Press, Cambridge (1983).

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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