Polynomial invariants of quantum codes
| dc.creator | Rains, Eric M. | |
| dc.date | 1997-04-24 | |
| dc.date.accessioned | 2026-07-07T06:14:14Z | |
| dc.date.available | 2026-07-07T06:14:14Z | |
| dc.description | The weight enumerators (quant-ph/9610040) of a quantum code are quite powerful tools for exploring its structure. As the weight enumerators are quadratic invariants of the code, this suggests the consideration of higher-degree polynomial invariants. We show that the space of degree k invariants of a code of length n is spanned by a set of basic invariants in one-to-one correspondence with S_k^n. We then present a number of equations and inequalities in these invariants; in particular, we give a higher-order generalization of the shadow enumerator of a code, and prove that its coefficients are nonnegative. We also prove that the quartic invariants of a ((4,4,2)) are uniquely determined, an important step in a proof that any ((4,4,2)) is additive ([2]). | |
| dc.description | 10 pages, AMSTeX | |
| dc.identifier | https://arxiv.org/abs/quant-ph/9704042 | |
| dc.identifier | http://arxiv.org/abs/quant-ph/9704042 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/93388 | |
| dc.subject | Quantum Physics | |
| dc.title | Polynomial invariants of quantum codes | |
| dc.type | text |