Recursive constructions for large caps
نویسنده
چکیده
We introduce several recursive constructions for caps in projective spaces. These generalize the known constructions in an essential way and lead to new large caps in many cases. Among our results we mention the construction of {(q + 1)(q2 + 3)}−caps in PG(5, q), of {q4 + 2q2}-caps in PG(6, q) and of q2(q2 + 1)2-caps in PG(9, q).
منابع مشابه
Constructions of Small Complete Caps in Binary Projective Spaces
In the binary projective spaces PG(n,2) k-caps are called large if k > 2n−1 and small if k ≤ 2n−1. In this paper we propose new constructions producing infinite families of small binary complete caps.
متن کاملThe structure of quaternary quantum caps
We give a geometric description of binary quantum stabilizer codes. In the case of distance d = 4 this leads to the notion of a quaternary quantum cap. We describe several recursive constructions for quantum caps, determine the quantum caps in PG(3, 4) and the cardinalities of quantum caps in PG(4, 4). ∗research partially supported NSA grant H98230-10-1-0159 †The research of this author takes p...
متن کاملLarge Caps in Small Spaces
We construct large caps in projective spaces of small dimension (up to 11) defined over fields of order at most 9. The constructions are both theoretical and computer-supported. Some more computergenerated 4-dimensional caps over larger fields are also mentioned.
متن کاملEntanglement-assisted Quantum Codes of Distance Four Constructed from Caps in PG(5,4) and PG(6,4)
The entanglement-assisted (EA) formalism is a generalization of the standard stabilizer formalism, and it can transform classical linear quaternary codes into entanglement-assisted quantum error correcting codes (EAQECCs) by using of shared entangled qubits between the sender and the receiver. In this work, we give elementary recursive constructions of special quaternary codes of length n and d...
متن کاملLarge sets of t-designs through partitionable sets, a review
The method of partitionable sets for constructing large sets of t-designs have now been used for nearly a decade. The method has resulted in some powerful recursive constructions and also existence results especially for large sets of prime sizes. Perhaps the main feature of the approach is its simplicity. In this paper, we describe the approach and show how it is employed to obtain some of the...
متن کامل