… lattice corresponding to a degenerate torus in X and completely characterize when its lattice
ideal … We compute dimension and length of some generalized toric codes defined on these …

… is the vanishing ideal of the … lattice ideals as their vanishing ideals. We present recent
results for obtaining a basis for the lattice and for computing a minimal generating set of its ideal. …

… of a projective space and a standard homogeneous lattice ideal of dimension one. We also
… lattice ideals. As application, we compute the main parameters of generalized toric codes on …

… of a toric code by evaluating at the full set of Fq-rational points X(Fq) in [26] and [27]. There
is yet another extension of classical toric codes, which we introduce now. As in the toric case, …

… how the topological order of the Toric Code appears when the lattice on which it is
defined … review of the traditional two-dimensional Toric Code, with an emphasis on how its …

… However groups are in some sense far too ideal as they only … lattice gauge theories [67,68],
we will construct the lattice … model, namely the Z2 toric code. Groupoid algebras are non-…

… code obtained from a general smooth toric variety by using Iα(Y ). Let I(Y ) be the ideal …
We use commutative algebraic tools such as the multigraded Hilbert polynomials of ideals …

… of the code corresponding to a set S will be the same as that of the code corresponding to
… , 28 ] generalized toric code over F 8 , better than any previously known code according to M…

… In general, an ideal code will have minimum distance and dimension large with respect
to its block length. Restating these parameters with this in mind, we will consider the relative …

… We will first focus on the toric code, assuming ideal (error-free) syndrome extraction. The
problem is first formed as a graph. The observed eigenvalue changes form the nodes on a …