engleski

Pairwise balanced designs and periodic Golay pairs

In this talk we exploit a relationship between certain pairwise balanced designs (PBDs) with v points and periodic Golay pairs (PGPs) of length v, to classify PGPs of length less than 40. PBDs are constructed using orbit matrices of subgroups of a cyclic group acting on the designs, which corresponds to some compression techniques for complementary sequences introduced by Đoković and Kotsireas. We use similar tools to construct new PGPs of lengths greater than 40 where classifications remain incomplete, and demonstrate that under some extra conditions on an automorphism group of the corresponding PBD, a PGP of length 90 will not exist. Length 90 remains the smallest length for which existence of a periodic Golay pair is undecided. Further, we show that under certain conditions the incidence and orbit matrices of PBDs related to PGPs span quasi-cyclic self-orthogonal codes.

periodic Golay pair ; pairwise balanced design ; automorphism group

nije evidentirano