当前位置: X-MOL 学术Des. Codes Cryptogr. › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
Flag-transitive, point-imprimitive 2- $$(v,k,\lambda )$$ ( v , k , λ ) symmetric designs with k and $$\lambda $$ λ prime powers
Designs, Codes and Cryptography ( IF 1.4 ) Pub Date : 2021-04-07 , DOI: 10.1007/s10623-021-00869-5
Jianfu Chen , Shenglin Zhou

Let \({\mathcal {D}}\) be a 2-\((v,k,\lambda )\) symmetric design with k and \(\lambda \) prime powers. If \({\mathcal {D}}\) admits a flag-transitive, point-imprimitive automorphism group G, we show that both k and \(\lambda \) must be powers of 2. Moreover, there exists an integer m such that either (a) \({\mathcal {D}}\) has parameters \((v,k,\lambda )=(2^{2m+2}-1, 2^{2m+1}, 2^{2m})\), and G preserves a partition of the points into \(2^{m+1}+1\) classes of size \(2^{m+1}-1\), or (b) \({\mathcal {D}}\) has parameters \((v,k,\lambda )=((2^{2m-1}-2^m+1)(2^{m-1}+1),\ 2^{2m-1},\ 2^m)\), and G preserves a partition of the points into \(2^{2m-1}-2^m+1\) classes of size \(2^{m-1}+1\).



中文翻译:

带有k和$$ \ lambda $$λ素数幂的标志传递,点-本原2- $$(v,k,\ lambda)$$(v,k,λ)对称设计

\({\ mathcal {d}} \)是2- \((V,K,\拉姆达)\)的对称设计具有ķ\(\拉姆达\)素权力。如果\({\ mathcal {D}} \)允许一个标志传递,点同质自同构群G,则表明k\(\ lambda \)都必须是2的幂。此外,存在一个整数m这样(a)\ {{\ mathcal {D}} \)的参数\((v,k,\ lambda)=(2 ^ {2m + 2} -1,2 ^ {2m + 1},2 ^ {2m})\)G将点的划分保留为大小为\(2 ^ {m + 1} -1 \)的\(2 ^ {m + 1} +1 \)类。或(b)\({\ mathcal {D}} \)的参数\((v,k,\ lambda)=(((2 ^ {2m-1} -2 ^ m + 1)(2 ^ {m -1} +1),\ 2 ^ {2m-1},\ 2 ^ m)\)G将点的分区保留为\(2 ^ {2m-1} -2 ^ m + 1 \)大小为\(2 ^ {m-1} +1 \)的类

更新日期:2021-04-08
down
wechat
bug