Naslov
PD-sets for codes related to flag-transitive symmetric designs

Autori
Crnković, Dean ; Mostarac, Nina

Izvornik
Transactions on combinatorics (2251-8657) 7 (2018), 1; 37-50

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
Code, graph ; flag-transitive design ; permutation decoding
(Code ; graph ; flag-transitive design ; permutation decoding)

Sažetak
For any prime p let $C_p(G)$ be the p-ary code spanned by the rows of the incidence matrix G of a graph $\Gamma$. Let $\Gamma$ be the incidence graph of a flag-transitive symmetric design D. We show that any flag-transitive automorphism group of D can be used as a PD-set for full error correction for the linear code Cp(G) (with any information set). It follows that such codes derived from flag-transitive symmetric designs can be decoded using permutation decoding. In that way to each flag- transitive symmetric $(v, k, \lambda )$ design we associate a linear code of length vk that is permutation decodable. PD-sets obtained in the described way are usually of large cardinality. By studying codes arising from some flag- transitive symmetric designs we show that smaller PD-sets can be found for specifi c information sets.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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