New Quantum Caps in PG(4, 4)

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 G F ( 4 ) . In this paper, we determine the values k such that there exists a quantum k ‐cap in P G ( 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 P G ( 4 , 4 ) not already known in the literature.