Entanglement-assisted Quantum Codes of Distance Four Constructed from Caps in PG(5,4) and PG(6,4)
نویسندگان
چکیده
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 dual distance four that constructed from known caps in projective space PG(5,4) and PG(6,4) for all length 6n283. Consequently, good maximal entanglement EAQECCs of minimum distance four for such length n are constructed from the obtained quaternary codes. Index Terms EAQECCs, maximal entanglement, quaternary code, cap.
منابع مشابه
New quantum caps in PG ( 4 , 4 )
Calderbank, Rains, Shor and Sloane (see [9]) showed that error-correction is possible in the context of quantum computations. Quantum stabilizer codes are a class of additive quaternary codes in binary projective spaces, which are self-orthogonal with respect to the symplectic form. A geometric description is given in [6], where also the notion of quantum cap is introduced. Quantum caps corresp...
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 کامل7 M ay 2 00 9 New quantum caps in PG ( 4 , 4
Calderbank, Rains, Shor and Sloane (see [6]) showed that error-correction is possible in the context of quantum computations. Quantum stabilizer codes are a class of additive quaternary codes in binary projective spaces, which are self-orthogonal with respect to the symplectic form. A geometric description is given in [5], where also the notion of quantum cap is introduced. Quantum caps corresp...
متن کاملExtensions of Generalized Product Caps
We give some variants of a new construction for caps. As an application of these constructions we obtain a 1216–cap in PG(9, 3) a 6464–cap in PG(11, 3) and several caps in ternary affine spaces of larger dimension, which lead to better asymptotics than the caps constructed by Calderbank and Fishburn [1]. These asymptotic improvements become visible in dimensions as low as 62, whereas the bound ...
متن کاملEntanglement-assisted quantum MDS codes constructed from negacyclic codes
Recently, entanglement-assisted quantum error correcting codes (EAQECCs) have been constructed by cyclic codes and negacyclic codes. In this paper, by analyzing the cyclotomic cosets in the defining set of constacyclic codes, we constructed three classes of new EAQECCs which satisfy the entanglement-assisted quantum Singleton bound. Besides, three classes of EAQECCs with maximal entanglement fr...
متن کامل