216 research outputs found
Z_q(Z_q+uZ_q)-Linear Skew Constacyclic Codes
In this paper, we study skew constacyclic codes over the ring where , for a prime and We give the definition of these codes as subsets of the ring . Some structural properties of the skew polynomial ring are discussed, where is an automorphism of We describe the generator polynomials of skew constacyclic codes over also we determine their minimal spanning sets and their sizes. Further, by using the Gray images of skew constacyclic codes over we obtained some new linear codes over . Finally, we have generalized these codes to double skew constacyclic codes over
On ZpZp[u, v]-additive cyclic and constacyclic codes
Let be the ring of residue classes modulo a prime . The
-additive cyclic codes of length
is identify as -submodule of
where
with
. In this article, we obtain the complete sets of
generator polynomials, minimal generating sets for cyclic codes with length
over and
-additive cyclic codes with length
respectively. We show that the Gray image of
-additive cyclic code with length
is either a QC code of length with index or a
generalized QC code of length over .
Moreover, some structural properties like generating polynomials, minimal
generating sets of -additive constacyclic
code with length are determined.Comment: It is submitted to the journa
Application of Constacyclic codes to Quantum MDS Codes
Quantum maximal-distance-separable (MDS) codes form an important class of
quantum codes. To get -ary quantum MDS codes, it suffices to find linear MDS
codes over satisfying by the
Hermitian construction and the quantum Singleton bound. If
, we say that is a dual-containing code. Many new
quantum MDS codes with relatively large minimum distance have been produced by
constructing dual-containing constacyclic MDS codes (see \cite{Guardia11},
\cite{Kai13}, \cite{Kai14}). These works motivate us to make a careful study on
the existence condition for nontrivial dual-containing constacyclic codes. This
would help us to avoid unnecessary attempts and provide effective ideas in
order to construct dual-containing codes. Several classes of dual-containing
MDS constacyclic codes are constructed and their parameters are computed.
Consequently, new quantum MDS codes are derived from these parameters. The
quantum MDS codes exhibited here have parameters better than the ones available
in the literature.Comment: 16 page
Entanglement phases as holographic duals of anyon condensates
Anyon condensation forms a mechanism which allows to relate different
topological phases. We study anyon condensation in the framework of Projected
Entangled Pair States (PEPS) where topological order is characterized through
local symmetries of the entanglement. We show that anyon condensation is in
one-to-one correspondence to the behavior of the virtual entanglement state at
the boundary (i.e., the entanglement spectrum) under those symmetries, which
encompasses both symmetry breaking and symmetry protected (SPT) order, and we
use this to characterize all anyon condensations for abelian double models
through the structure of their entanglement spectrum. We illustrate our
findings with the Z4 double model, which can give rise to both Toric Code and
Doubled Semion order through condensation, distinguished by the SPT structure
of their entanglement. Using the ability of our framework to directly measure
order parameters for condensation and deconfinement, we numerically study the
phase diagram of the model, including direct phase transitions between the
Doubled Semion and the Toric Code phase which are not described by anyon
condensation.Comment: 20+7 page
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