Bounds on subspace codes based on totally isotropic subspace in symplectic spaces and extended symplectic spaces

In this paper, we propose the Sphere-packing bound, Singleton bound and Gilbert–Varshamov bound on the subspace codes [Formula: see text] based on totally isotropic subspaces in symplectic space [Formula: see text] and on the subspace codes [Formula: see text] based on totally isotropic subspace in extended symplectic space [Formula: see text].

A CONSTRUCTION OF CARTESIAN AUTHENTICATION CODE FROM SINGULAR SYMPLECTIC SPACES OVER A FINITE FIELD

In this paper, we construct a Cartesian authentication code from subspaces of singular symplectic space [Formula: see text] and compute its parameters. Assuming that the encoding rules of the transmitter and the receiver are chosen according to a uniform probability distribution, the probabilities of successful impersonation attack and substitution attack are also computed.

Generalized Inverse of Upper Triangular Infinite Dimensional Hamiltonian Operators

In this paper, we deal with the generalized inverse of upper triangular infinite dimensional Hamiltonian operators. Based on the structure operator matrix J in infinite dimensional symplectic spaces, it is shown that the generalized inverse of an infinite dimensional Hamiltonian operator is also Hamiltonian. Further, using the decomposition of spaces, an upper triangular Hamiltonian operator can be written as a new operator matrix of order 3, and then an explicit expression of the generalized inverse is given.