PD-sets for codes related to flag-transitive symmetric designs
عنوان مقاله: PD-sets for codes related to flag-transitive symmetric designs
شناسه ملی مقاله: JR_COMB-7-1_005
منتشر شده در در سال 1397
شناسه ملی مقاله: JR_COMB-7-1_005
منتشر شده در در سال 1397
مشخصات نویسندگان مقاله:
Dean Crnkovic - Department of Mathematics, University of Rijeka, Radmile Matječić ۲, ۵۱۰۰۰ Rijeka, Croatia
Nina Mostarac - Department of Mathematics, University of Rijeka, Rijeka, Croatia
خلاصه مقاله:
Dean Crnkovic - Department of Mathematics, University of Rijeka, Radmile Matječić ۲, ۵۱۰۰۰ Rijeka, Croatia
Nina Mostarac - Department of Mathematics, University of Rijeka, Rijeka, Croatia
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 C_p(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 specific information sets.
کلمات کلیدی: Code, graph, flag-transitive design, permutation decoding
صفحه اختصاصی مقاله و دریافت فایل کامل: https://civilica.com/doc/1307326/