Calderbank, Rains, Shor and Sloane 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. Quantum caps correspond to the special case of quantum stabilizer codes of distance d=4 when the code is linear over GF(4). In this paper we have solved the open problem about the spectrum of pure linear quantum [[n,n-10,4]]-codes, proving the non existence for n=11,37,39. Besides we have shown that 20 is the minimum size of the complete caps in PG(4,4) and that a 20-complete cap is quantic.
The spectrum of linear pure quantum [[n,n-10,4]]-codes
BARTOLI, DANIELE;MARCUGINI, Stefano;PAMBIANCO, Fernanda
2010
Abstract
Calderbank, Rains, Shor and Sloane 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. Quantum caps correspond to the special case of quantum stabilizer codes of distance d=4 when the code is linear over GF(4). In this paper we have solved the open problem about the spectrum of pure linear quantum [[n,n-10,4]]-codes, proving the non existence for n=11,37,39. Besides we have shown that 20 is the minimum size of the complete caps in PG(4,4) and that a 20-complete cap is quantic.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
