Entanglement-assisted quantum codes from Galois LCD codes

Entanglement-assisted quantum error-correcting codes (EAQECCs) make use of preexisting entanglement between the sender and receiver to boost the rate of transmission. It is possible to construct an EAQECC from any classical linear code, unlike standard quantum error-correcting codes, which can only be constructed from dual-containing codes. However, the parameter of ebits $c$ is usually calculated by computer search. In this paper, we construct four classes of MDS entanglement-assisted quantum error-correcting codes (MDS EAQECCs) based on $k$-Galois LCD MDS codes for some certain code lengths, where the parameter of ebits $c$ can be easily generated algebraically and not by computational search. Moreover, the constructed four classes of EAQECCs are also maximal-entanglement EAQECCs

On New Quantum Codes From Matrix Product Codes

In this paper, by using matrix product codes, several classes of new quantum codes are obtained. Moreover, some of them have better parameters than the previous quantum codes available.Comment: 12 page

The weight distribution of a family of p-ary cyclic codes

Let m, k be positive integers, p be an odd prime and $\pi$ be a primitive element of $\mathbb{F}_{p^m}$. In this paper, we determine the weight distribution of a family of cyclic codes $\mathcal{C}_t$ over $\mathbb{F}_p$, whose duals have two zeros $\pi^{-t}$ and $-\pi^{-t}$, where $t$ satisfies $t\equiv \frac{p^k+1}{2}p^\tau \ ({\rm mod}\ \frac{p^m-1}{2})$ for some $\tau \in \{0,1,\cdots, m-1\}$.Comment: 15 page

A class of pp-ary cyclic codes and their weight enumerators

Let $m$, $k$ be positive integers such that $\frac{m}{\gcd(m,k)}\geq 3$, $p$ be an odd prime and $\pi$ be a primitive element of $\mathbb{F}_{p^m}$. Let $h_1(x)$ and $h_2(x)$ be the minimal polynomials of $-\pi^{-1}$ and $\pi^{-\frac{p^k+1}{2}}$ over $\mathbb{F}_p$, respectively. In the case of odd $\frac{m}{\gcd(m,k)}$, when $k$ is even, $\gcd(m,k)$ is odd or when $\frac{k}{\gcd(m,k)}$ is odd, Zhou et~al. in \cite{zhou} obtained the weight distribution of a class of cyclic codes $\mathcal{C}$ over $\mathbb{F}_p$ with parity-check polynomial $h_1(x)h_2(x)$. In this paper, we further investigate this class of cyclic codes $\mathcal{C}$ over $\mathbb{F}_p$ in the rest case of odd $\frac{m}{\gcd(m,k)}$ and the case of even $\frac{m}{\gcd(m,k)}$. Moreover, we determine the weight distribution of cyclic codes $\mathcal{C}$.Comment: 22 page

Constant Composition Codes as Subcodes of Linear Codes

In this paper, on one hand, a class of linear codes with one or two weights is obtained. Based on these linear codes, we construct two classes of constant composition codes, which includes optimal constant composition codes depending on LVFC bound. On the other hand, a class of constant composition codes is derived from known linear codes.Comment: 13page

The existence of two closed characteristics on every compact star-shaped hypersurface in R4{\bf R}^4

Recently, Cristofaro-Gardiner and Hutchings proved that there exist at least two closed characteristics on every compact star-shaped hypersuface in ${\bf R}^4$. Then Ginzburg, Hein, Hryniewicz, and Macarini gave this result a second proof. In this paper, we give it a third proof by using index iteration theory, resonance identities of closed characteristics and a remarkable theorem of Ginzburg et al.Comment: To appear in Acta Mathematica Sinica, English Series (Special issue for the 29th anniversary of the establishment of the Shiing-Shen Chern Prize of the Chinese Mathematical Society). This is the final version. arXiv admin note: substantial text overlap with arXiv:1308.3543; and text overlap with arXiv:math/0701673 by other author

Constant composition codes derived from linear codes

In this paper, we propose a class of linear codes and obtain their weight distribution. Some of these codes are almost optimal. Moreover, several classes of constant composition codes(CCCs) are constructed as subcodes of linear codes.Comment: 13 page

Automated identification and characterization of parcels (AICP) with OpenStreetMap and Points of Interest

Against the paucity of urban parcels in China, this paper proposes a method to automatically identify and characterize parcels (AICP) with OpenStreetMap (OSM) and Points of Interest (POI) data. Parcels are the basic spatial units for fine-scale urban modeling, urban studies, as well as spatial planning. Conventional ways of identification and characterization of parcels rely on remote sensing and field surveys, which are labor intensive and resource-consuming. Poorly developed digital infrastructure, limited resources, and institutional barriers have all hampered the gathering and application of parcel data in developing countries. Against this backdrop, we employ OSM road networks to identify parcel geometries and POI data to infer parcel characteristics. A vector-based CA model is adopted to select urban parcels. The method is applied to the entire state of China and identifies 82,645 urban parcels in 297 cities. Notwithstanding all the caveats of open and/or crowd-sourced data, our approach could produce reasonably good approximation of parcels identified from conventional methods, thus having the potential to become a useful supplement.Comment: 26 pages, 6 figure

Duality and Recycling Computing in Quantum Computers

Quantum computer possesses quantum parallelism and offers great computing power over classical computer \cite{er1,er2}. As is well-know, a moving quantum object passing through a double-slit exhibits particle wave duality. A quantum computer is static and lacks this duality property. The recently proposed duality computer has exploited this particle wave duality property, and it may offer additional computing power \cite{r1}. Simply put it, a duality computer is a moving quantum computer passing through a double-slit. A duality computer offers the capability to perform separate operations on the sub-waves coming out of the different slits, in the so-called duality parallelism. Here we show that an $n$-dubit duality computer can be modeled by an $(n+1)$-qubit quantum computer. In a duality mode, computing operations are not necessarily unitary. A $n$-qubit quantum computer can be used as an $n$-bit reversible classical computer and is energy efficient. Our result further enables a $(n+1)$-qubit quantum computer to run classical algorithms in a $O(2^n)$-bit classical computer. The duality mode provides a natural link between classical computing and quantum computing. Here we also propose a recycling computing mode in which a quantum computer will continue to compute until the result is obtained. These two modes provide new tool for algorithm design. A search algorithm for the unsorted database search problem is designed.Comment: 4 pages and 3 figure

Deleting a marked item from an unsorted database with a single query

In this Letter we present a quantum deletion algorithm that deletes a marked state from an unsorted database of $N$ items with only a single query. This algorithm achieves exponential speedup compared with classical algorithm where O(N) number of query is required. General property of this deleting algorithm is also studied.Comment: 4 pages and 1 figur