Calderbank, Rains, Shor, and Sloane (see [10]) showed that quantum stabilizer codes correspond to additive quaternary codes in binary projective spaces, which are self-orthogonal with respect to the symplectic form. A geometric description is given in [8, 19]. In [8] the notion of a quantum cap is introduced. Quantum caps are equivalent to quantum stabilizer codes of minimum distance d=4 when the code is linear over GF(4). In this paper, we determine the values k such that there exists a quantum k-cap in PG(4,4), corresponding to pure linear [[n,n-10,4]] quantum codes, proving, by exhaustive search, that no 11, 37, 39-quantum caps exist. Moreover we give examples of quantum caps in PG(4,4) not already known in the literature.
New quantum caps in PG(4,4)
BARTOLI, DANIELE;FAINA, Giorgio;MARCUGINI, Stefano;PAMBIANCO, Fernanda
2012
Abstract
Calderbank, Rains, Shor, and Sloane (see [10]) showed that quantum stabilizer codes correspond to additive quaternary codes in binary projective spaces, which are self-orthogonal with respect to the symplectic form. A geometric description is given in [8, 19]. In [8] the notion of a quantum cap is introduced. Quantum caps are equivalent to quantum stabilizer codes of minimum distance d=4 when the code is linear over GF(4). In this paper, we determine the values k such that there exists a quantum k-cap in PG(4,4), corresponding to pure linear [[n,n-10,4]] quantum codes, proving, by exhaustive search, that no 11, 37, 39-quantum caps exist. Moreover we give examples of quantum caps in PG(4,4) not already known in the literature.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
