Motivated by the applications to generalized Howell designs and multiply constant-weight codes, we establish an asymptotic existence theorem for(k, λ)-frames of type g^n with a pair of orthogonal frame resolutions vi...Motivated by the applications to generalized Howell designs and multiply constant-weight codes, we establish an asymptotic existence theorem for(k, λ)-frames of type g^n with a pair of orthogonal frame resolutions via decompositions of edge-colored complete digraphs into prescribed edge-colored subgraphs.展开更多
In this paper, it is shown that the necessary conditions for the existence of a ( gv, {g, 3 α }, 3, λ)-DF in Z gv for α∈ {0, 1, 2} are also sufficient with two exceptions of (v, g, λ, α) = (9, 1, 1, 1), (9, 1, 2...In this paper, it is shown that the necessary conditions for the existence of a ( gv, {g, 3 α }, 3, λ)-DF in Z gv for α∈ {0, 1, 2} are also sufficient with two exceptions of (v, g, λ, α) = (9, 1, 1, 1), (9, 1, 2, 2). Finally, the existence spectrum of a cyclic (3, λ)-GDD of type g v is determined.展开更多
基金supported by National Natural Science Foundation of China(Grant Nos.11431003 and 11471032)Fundamental Research Funds for the Central Universities(Grant Nos.2016JBM071 and 2016JBZ012)
文摘Motivated by the applications to generalized Howell designs and multiply constant-weight codes, we establish an asymptotic existence theorem for(k, λ)-frames of type g^n with a pair of orthogonal frame resolutions via decompositions of edge-colored complete digraphs into prescribed edge-colored subgraphs.
基金supported by National Natural Science Foundation of China (Grant No.10771013 and 10831002)
文摘In this paper, it is shown that the necessary conditions for the existence of a ( gv, {g, 3 α }, 3, λ)-DF in Z gv for α∈ {0, 1, 2} are also sufficient with two exceptions of (v, g, λ, α) = (9, 1, 1, 1), (9, 1, 2, 2). Finally, the existence spectrum of a cyclic (3, λ)-GDD of type g v is determined.
