The packing of pairs by quadruples
Discrete Mathematics
A new class of group divisible designs with block size three
Journal of Combinatorial Theory Series A
Some recent developments on BIBDs and related designs
Discrete Mathematics - Special issue on discrete mathematics in China
Linear spaces with many small lines
Proceedings of the first International conference on Linear spaces
Pairwise Balanced Designs with Consecutive Block Sizes
Designs, Codes and Cryptography
Existence of Incomplete Transversal Designs with BlockSize Five and Any Index λ
Designs, Codes and Cryptography
Optimal constant weight codes over Zk and generalized designs
Discrete Mathematics
Inductive Constructions of Perfect Ternary Constant-Weight Codes with Distance 3
Problems of Information Transmission
Constant Weight Codes and Group Divisible Designs
Designs, Codes and Cryptography
A Class of Perfect Ternary Constant-Weight Codes
Designs, Codes and Cryptography
On Perfect Ternary Constant Weight Codes
Designs, Codes and Cryptography
On Group-Divisible Designs with Block Size Four and Group-Type gum1
Designs, Codes and Cryptography
Group divisible designs with block size four and group type gum1 with minimum m
Designs, Codes and Cryptography
Existence of Generalized Steiner Systems GS(2,4,",2)
Designs, Codes and Cryptography
Super-simple (ν, 5, 5) Designs
Designs, Codes and Cryptography
Handbook of Combinatorial Designs, Second Edition (Discrete Mathematics and Its Applications)
Handbook of Combinatorial Designs, Second Edition (Discrete Mathematics and Its Applications)
Discrete Applied Mathematics
Super-simple Steiner pentagon systems
Discrete Applied Mathematics
Discrete Applied Mathematics
Optimal ternary constant-weight codes of weight four and distance six
IEEE Transactions on Information Theory
A lower bound for ternary constant weight codes
IEEE Transactions on Information Theory
On the constructions of constant-weight codes
IEEE Transactions on Information Theory
On the Svanstrom bound for ternary constant-weight codes
IEEE Transactions on Information Theory
Bounds and constructions for ternary constant-composition codes
IEEE Transactions on Information Theory
Constructions for q-Ary Constant-Weight Codes
IEEE Transactions on Information Theory
The Sizes of Optimal -Ary Codes of Weight Three and Distance Four: A Complete Solution
IEEE Transactions on Information Theory
A pair of disjoint 3-GDDs of type gtu1
Designs, Codes and Cryptography
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A design is said to be super-simple if the intersection of any two blocks has at most two elements. A super-simple design $${\mathcal{D}}$$ with point set X, block set $${\mathcal{B}}$$ and index 驴 is called completely reducible super-simple (CRSS), if its block set $${\mathcal{B}}$$ can be written as $${\mathcal{B}=\bigcup_{i=1}^{\lambda} \mathcal{B}_i}$$ , such that $${\mathcal{B}_i}$$ forms the block set of a design with index unity but having the same parameters as $${\mathcal{D}}$$ for each 1 驴 i 驴 驴. It is easy to see, the existence of CRSS designs with index 驴 implies that of CRSS designs with index i for 1 驴 i 驴 驴. CRSS designs are closely related to q-ary constant weight codes (CWCs). A (v, 4, q)-CRSS design is just an optimal (v, 6, 4) q+1 code. On the other hand, CRSS group divisible designs (CRSSGDDs) can be used to construct q-ary group divisible codes (GDCs), which have been proved useful in the constructions of q-ary CWCs. In this paper, we mainly investigate the existence of CRSS designs. Three neat results are obtained as follows. Firstly, we determine completely the spectrum for a (v, 4, 3)-CRSS design. As a consequence, a class of new optimal (v, 6, 4)4 codes is obtained. Secondly, we give a general construction for (4, 4)-CRSSGDDs with skew Room frames, and prove that the necessary conditions for the existence of a (4, 2)-CRSSGDD of type g u are also sufficient except definitely for $${(g,u)\in \{(2,4),(3,4),(6,4)\}}$$ . Finally, we consider the related optimal super-simple (v, 4, 2)-packings and show that such designs exist for all v 驴 4 except definitely for $${v\in \{4,5,6,9\}}$$ .