We present a generalization of quantum error correction to infinite-dimensional Hilbert spaces. The generalization yields new classes of quantum error correcting codes that have no finite-dimensional counterparts. The error correction theory we develop begins with a shift of focus from states to algebras of observables. Standard subspace codes and subsystem codes are seen as the special case of...

In this paper we extend to asymmetric quantum error-correcting codes (AQECC) the construction methods, namely: puncturing, extending, expanding, direct sum and the (u|u + v) construction. By applying these methods, several families of asymmetric quantum codes can be constructed. Consequently, as an example of application of quantum code expansion developed here, new families of asymmetric quant...

We propose a new approach to study the evolution of a quantum state that is encoded in a system which is continuously subject to the operations required to implement a quantum error correcting code. In the limit of continuous error correction we introduce a Markovian master equation that includes the effects of: a) Hamiltonian evolution, b) errors caused by the interaction with an environment a...

We examine the performance of quantum error correcting codes subjected to random Haar distribution transformations of weight t. Rather than requiring correction of all errors, we require some high probability that a random error is corrected. We find that, for any integer i and arbitrarily high probability p < 1, there are codes which perfectly correct errors up to weight t and can correct erro...

The economic transition in China poses new questions in studying product demand. In this study, we investigate the demand pattern and structural changes during the economic transformation using annual data from the paper and paperboard industry in China. Instrumental variable estimations as well as cointegration analysis and error-correction models are applied to the analysis. Our results show ...

Abstract. We treat toric surfaces and their application to construction of error-correcting codes and determination of the parameters of the codes, surveying and expanding the results of [4]. For any integral convex polytope in R there is an explicit construction of a unique error-correcting code of length (q − 1) over the finite field Fq. The dimension of the code is equal to the number of int...

We replace the usual setting for error-correcting codes (i.e. vector spaces over finite fields) with that of permutation groups. We give an algorithm which uses a combinatorial structure which we call an uncovering-by-bases, related to covering designs, and construct some examples of these. We also analyse the complexity of the algorithm. We then formulate a conjecture about uncoverings-by-base...

A (k; n)-arc in PG(2; q) is usually deened to be a set K of k points in the plane such that some line meets K in n points but such that no line meets K in more than n points. There is an extensive literature on the topic of (k; n)-arcs. Here we keep the same deenition but allow K to be a multiset, that is, permit K to contain multiple points. The case k = q 2 + q + 2 is of interest because it i...

In this paper we use intersection theory to develop methods for obtaining lower bounds on the parameters of algebraic geometric error-correcting codes constructed from varieties of arbitrary dimension. The methods are sufficiently general to encompass many of the codes previously constructed from higherdimensional varieties, as well as those coming from curves. And still, the bounds obtained ar...