Yayınlanmış 1 Ocak 2018
| Sürüm v1
Dergi makalesi
Açık
Toric codes and lattice ideals
Açıklama
Let X be a complete simplicial toric variety over a finite field F-q with homogeneous coordinate ring S = F-q [x(1),., x(r)] and split torus T-X congruent to (F*(q))(n). We prove that submonoids of T-X are exactly those subsets that are parameterized by Laurents monomials. We give an algorithm for determining this parametrization if the submonoid is the zero locus of a lattice ideal in the torus. We also show that vanishing ideals of submonoids of T-X are radical homogeneous lattice ideals of dimension r - n. We identify the lattice corresponding to a degenerate torus in X and completely characterize when its lattice ideal is a complete intersection. We compute dimension and length of some generalized toric codes defined on these degenerate tori. (C) 2018 Elsevier Inc. All rights reserved.
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