Related papers: Quantum Cyclic Code of length dividing $p^{t}+1$
The importance of quantum error correction in paving the way to build a practical quantum computer is no longer in doubt. This dissertation makes a threefold contribution to the mathematical theory of quantum error-correcting codes.…
We show that within any quantum stabilizer code there lurks a classical binary linear code with similar error-correcting capabilities, thereby demonstrating new connections between quantum codes and classical codes. Using this result --…
We study the hardness of the problem of finding the distance of quantum error-correcting codes. The analogous problem for classical codes is known to be NP-hard, even in approximate form. For quantum codes, various problems related to…
We describe a general method for turning quantum circuits into sparse quantum subsystem codes. The idea is to turn each circuit element into a set of low-weight gauge generators that enforce the input-output relations of that circuit…
In this paper, we study skew cyclic codes with arbitrary length over the ring $R=\mathbb{F}_{p}+u\mathbb{F}_{p}$ where $p$ is an odd prime and $% u^{2}=0$. We characterize all skew cyclic codes of length $n$ as left $% R[x;\theta…
Quantum error correction and the use of quantum error correction codes is likely to be essential for the realisation of practical quantum computing. Because the error models of quantum devices vary widely, quantum codes which are tailored…
Although qubit coherence times and gate fidelities are continuously improving, logical encoding is essential to achieve fault tolerance in quantum computing. In most encoding schemes, correcting or tracking errors throughout the computation…
In this note, we present a construction of new nonbinary quantum codes with good parameters. These codes are obtained by applying the Calderbank-Shor-Steane (CSS) construction. In order to do this, we show the existence of (classical)…
BCH codes are an interesting class of cyclic codes due to their efficient encoding and decoding algorithms. In many cases, BCH codes are the best linear codes. However, the dimension and minimum distance of BCH codes have been seldom…
The permutation groups of cyclic codes are widely applicable in determining the weight distribution of codes, decoding theory and various other areas. In this paper, by employing two distinct matrix representations, we can relate cyclic…
In this article, we investigate properties of cyclic codes over a finite non-chain ring $\mathbb{F}_q+v\mathbb{F}_q+v^2\mathbb{F}_q+v^3\mathbb{F}_q+v^4\mathbb{F}_q,$ where $q=p^r,$ $r$ is a positive integer, $p$ is an odd prime, $4 \mid…
Let $q$ be a prime power and let $\mathcal{R}=\mathbb{F}_{q}[u_1,u_2, \cdots, u_k]/\langle f_i(u_i),u_iu_j-u_ju_i\rangle$ be a finite non-chain ring, where $f_i(u_i), 1\leq i \leq k$ are polynomials, not all linear, which split into…
In this paper, cyclic codes are established over some finite quaternion integer rings with respect to the quaternion Mannheim distance, and de- coding algorithm for these codes is given.
This paper provides a comprehensive analysis of almost maximum distance separable (AMDS) constacyclic codes of length $4p^{\varsigma}$ over the finite field $\mathbb{F}_{p^m}$, where $p$ is an odd prime number. Furthermore, it introduces…
We describe the theory of quantum convolutional error correcting codes. These codes are aimed at protecting a flow of quantum information over long distance communication. They are largely inspired by their classical analogs which are used…
In an interesting paper Professor Cunsheng Ding provided three constructions of cyclic codes of length being a product of two primes. Numerical data shows that many codes from these constructions are best cyclic codes of the same length and…
We characterize constacyclic codes in the spectral domain using the finite field Fourier transform (FFFT) and propose a reduced complexity method for the spectral-domain decoder. Further, we also consider repeated-root constacyclic codes…
One formidable difficulty in quantum communication and computation is to protect information-carrying quantum states against undesired interactions with the environment. In past years, many good quantum error-correcting codes had been…
In this work, we introduce a technique for reducing the length of a quantum stabilizer code, and we call this deflation of the code. Deflation can be seen as a generalization of the well-known puncturing and shortening techniques in cases…
In this paper, we give a constructive proof to show that if there exist a classical linear code C is a subset of F_q^n of dimension k and a classical linear code D is a subset of F_q^k^m of dimension s, where q is a power of a prime number…