Kerdock Codes Determine Unitary 2-Designs

The non-linear binary Kerdock codes are known to be Gray images of certain extended cyclic codes of length $N = 2^m$ over $\mathbb{Z}_4$. We show that exponentiating these $\mathbb{Z}_4$-valued codewords by $\imath \triangleq \sqrt{-1}$ produces stabilizer states, that are quantum states obtained using only Clifford unitaries. These states are also the common eigenvectors of commuting Hermitian matrices forming maximal commutative subgroups (MCS) of the Pauli group. We use this quantum description to simplify the derivation of the classical weight distribution of Kerdock codes. Next, we organize the stabilizer states to form $N+1$ mutually unbiased bases and prove that automorphisms of the Kerdock code permute their corresponding MCS, thereby forming a subgroup of the Clifford group. When represented as symplectic matrices, this subgroup is isomorphic to the projective special linear group PSL($2,N$). We show that this automorphism group acts transitively on the Pauli matrices, which implies that the ensemble is Pauli mixing and hence forms a unitary $2$-design. The Kerdock design described here was originally discovered by Cleve et al. (arXiv:1501.04592), but the connection to classical codes is new which simplifies its description and translation to circuits significantly. Sampling from the design is straightforward, the translation to circuits uses only Clifford gates, and the process does not require ancillary qubits. Finally, we also develop algorithms for optimizing the synthesis of unitary $2$-designs on encoded qubits, i.e., to construct logical unitary $2$-designs. Software implementations are available at https://github.com/nrenga/symplectic-arxiv18a, which we use to provide empirical gate complexities for up to $16$ qubits.Comment: 16 pages double-column, 4 figures, and some circuits. Accepted to 2019 Intl. Symp. Inf. Theory (ISIT), and PDF of the 5-page ISIT version is included in the arXiv packag

Deterministically Computing Reduction Numbers of Polynomial Ideals

We discuss the problem of determining reduction number of a polynomial ideal I in n variables. We present two algorithms based on parametric computations. The first one determines the absolute reduction number of I and requires computation in a polynomial ring with (n-dim(I))dim(I) parameters and n-dim(I) variables. The second one computes via a Grobner system the set of all reduction numbers of the ideal I and thus in particular also its big reduction number. However,it requires computations in a ring with n.dim(I) parameters and n variables.Comment: This new version replaces the earlier version arXiv:1404.1721 and it has been accepted for publication in the proceedings of CASC 2014, Warsaw, Polna

Real-time Optimal Resource Allocation for Embedded UAV Communication Systems

We consider device-to-device (D2D) wireless information and power transfer systems using an unmanned aerial vehicle (UAV) as a relay-assisted node. As the energy capacity and flight time of UAVs is limited, a significant issue in deploying UAV is to manage energy consumption in real-time application, which is proportional to the UAV transmit power. To tackle this important issue, we develop a real-time resource allocation algorithm for maximizing the energy efficiency by jointly optimizing the energy-harvesting time and power control for the considered (D2D) communication embedded with UAV. We demonstrate the effectiveness of the proposed algorithms as running time for solving them can be conducted in milliseconds.Comment: 11 pages, 5 figures, 1 table. This paper is accepted for publication on IEEE Wireless Communications Letter

Vietnam\u27s Entire People Ownership of Land: Theory and Practice

The Constitution of Vietnam declares that “[t]he Socialist Republic of Vietnam State is a socialist rule of law State of the People, by the People, and for the People.” It also states that land is “under ownership by the entire people represented and uniformly managed by the State.” This means the entire people of Vietnam are collective landowners and the Vietnam State is their “representative.” Given that, how might the public execute its real ownership—rather than treating “people’s ownership” as just a slogan? This article analyzes the gaps in theory and practice in Vietnam, a country with a robust market economy where land user rights are marketable despite the lack of private land ownership rights. It reviews current Vietnamese land law and makes recommendations for reducing uncertainty about “entire people ownership,” and increasing the transparency and overall legitimacy of the legal regime governing private use of land. Specifically, the authors recommend that Vietnam grant lawful land users the status of “secondary owners” of land, effectively as co-owners with the State and with protected property ownership rights

Vietnam\u27s Entire People Ownership of Land: Theory and Practice

The Constitution of Vietnam declares that “[t]he Socialist Republic of Vietnam State is a socialist rule of law State of the People, by the People, and for the People.” It also states that land is “under ownership by the entire people represented and uniformly managed by the State.” This means the entire people of Vietnam are collective landowners and the Vietnam State is their “representative.” Given that, how might the public execute its real ownership—rather than treating “people’s ownership” as just a slogan? This article analyzes the gaps in theory and practice in Vietnam, a country with a robust market economy where land user rights are marketable despite the lack of private land ownership rights. It reviews current Vietnamese land law and makes recommendations for reducing uncertainty about “entire people ownership,” and increasing the transparency and overall legitimacy of the legal regime governing private use of land. Specifically, the authors recommend that Vietnam grant lawful land users the status of “secondary owners” of land, effectively as coowners with the State and with protected property ownership rights

The Right To Access Information on Land Recovery, Compensation, Assistance, And Resettlement: Case Study, City of Can Tho, Vietnam

Land recovery in Vietnam is the process of compulsory transfer of land use rights from the hands of land users to the hands of the State by way of local government agencies. Land recovery frequently raises issues of compensation, assistance, and resettlement. It is vital for affected land users and the general public to have access to reports on land recovery, compensation, and resettlement. The article describes a limited survey of Vietnamese people whose land was subject to government recovery and evaluates their access to and understanding of information at each stage of the land recovery process. The study revealed a number of weaknesses in the communication process between land users and state entities when government agencies recover property for public purposes. The article makes specific recommendations meant to balance the interests of the state, investors, and people subject to land recovery, and to ensure democracy and implementation of the Vietnamese public’s right to oversight and accountability

Crowdsourcing complex workflows under budget constraints

We consider the problem of task allocation in crowdsourcing systems with multiple complex workflows, each of which consists of a set of interdependent micro-tasks. We propose Budgeteer, an algorithm to solve this problem under a budget constraint. In particular, our algorithm first calculates an efficient way to allocate budget to each workflow. It then determines the number of inter-dependent micro-tasks and the price to pay for each task within each workflow, given the corresponding budget constraints. We empirically evaluate it on a well-known crowdsourcing-based text correction workflow using Amazon Mechanical Turk, and show that Budgeteer can achieve similar levels of accuracy to current benchmarks, but is on average 45% cheaper