Tight relative 2-designs on two shells in Johnson association schemes

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• 作者：Yan Zhu^a ; ^{zhuyan@sjtu.edu.cn" class="auth_mail" title="E-mail the corresponding author} ; Eiichi Bannai^a ; ^{bannai@sjtu.edu.cn" class="auth_mail" title="E-mail the corresponding author} ; Etsuko Bannai^b ; ^{et-ban@rc4.so-net.ne.jp" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Relative tt-design ; Tight design ; Johnson association scheme ; Coherent configuration
• 刊名：Discrete Mathematics
• 出版年：2016
• 出版时间：6 February 2016
• 年：2016
• 卷：339
• 期：2
• 页码：957-973
• 全文大小：483 K

文摘

There exist many tight relative 2-designs on two shells in binary Hamming association schemes b=MathURL&_method=retrieve&_eid=1-s2.0-S0012365X15003787&_mathId=si104.gif&_user=111111111&_pii=S0012365X15003787&_rdoc=1&_issn=0012365X&md5=be2633ac3be3b78fc8ead9dd5e87f579" title="Click to view the MathML source">H(n,2)$H(n,2)$ and each such design has the structure of a coherent configuration. In this paper, we study the existence problem of tight relative 2-designs on two shells in Johnson association schemes b=MathURL&_method=retrieve&_eid=1-s2.0-S0012365X15003787&_mathId=si105.gif&_user=111111111&_pii=S0012365X15003787&_rdoc=1&_issn=0012365X&md5=18231a26886c96cfcbe25398208281b0" title="Click to view the MathML source">J(v,k)$J(v,k)$. We determine all possible parameters of such designs for b=MathURL&_method=retrieve&_eid=1-s2.0-S0012365X15003787&_mathId=si106.gif&_user=111111111&_pii=S0012365X15003787&_rdoc=1&_issn=0012365X&md5=162fbda2c97a53464468b3ef57c747c9" title="Click to view the MathML source">v≤100$v\le 100$. For each case, we discuss whether such a design exists. Moreover, we construct some new tight relative 2-designs with constant weight in b=MathURL&_method=retrieve&_eid=1-s2.0-S0012365X15003787&_mathId=si105.gif&_user=111111111&_pii=S0012365X15003787&_rdoc=1&_issn=0012365X&md5=18231a26886c96cfcbe25398208281b0" title="Click to view the MathML source">J(v,k)$J(v,k)$. They are related to some specific symmetric 2-designs. All examples satisfying b=MathURL&_method=retrieve&_eid=1-s2.0-S0012365X15003787&_mathId=si106.gif&_user=111111111&_pii=S0012365X15003787&_rdoc=1&_issn=0012365X&md5=162fbda2c97a53464468b3ef57c747c9" title="Click to view the MathML source">v≤100$v\le 100$ have the structure of a coherent configuration.