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

Article Type:
Research/Original Article (دارای رتبه معتبر)
Abstract:
For any prime p let Cp(G) be the p-ary code spanned by the rows of the incidence matrix G of a graph Γý. ýLet Γ be the incidence graph of a flag-transitive symmetric design Dý. ýWe show that any flag-transitiveý ýautomorphism group of D can be used as a PD-set for full error correction for the linear code Cp(G)ý ý(with any information set)ý. ýIt follows that such codes derived from flag-transitive symmetric designs can beý ýdecoded using permutation decodingý. ýIn that way to each flag-transitive symmetric (vý,ýký,ýλ) design we associate a linear code of length vk that isý ýpermutation decodableý. ýPD-sets obtained in the described way are usually of large cardinalityý. ýBy studying codes arising from some flag-transitive symmetric designs we show that smaller PD-sets can be found forý ýspecific information setsý.
Language:
English
Published:
Transactions on Combinatorics, Volume:7 Issue: 1, Mar 2018
Pages:
37 to 50
https://www.magiran.com/p1787226