Related papers: Boundaries for the Honeycomb Code
High dimensional expanders simultaneously satisfying spectral and combinatorial (coboundary) expansion have recently played a major role in breakthroughs in PCP and coding theory, but the only known construction of such complexes is…
Topological subsystem codes proposed recently by Bombin are quantum error correcting codes defined on a two-dimensional grid of qubits that permit reliable quantum information storage with a constant error threshold. These codes require…
Single-shot error correction outperforms conventional approaches by requiring only one round of stabilizer measurements for decoding, even in the presence of measurement errors. This capability relates to the confinement property of codes,…
The Nahm pole boundary condition for certain gauge theory equations in four and five dimensions is defined by requiring that a solution should have a specified singularity along the boundary. In the present paper, we show that this boundary…
A generalized low-density parity-check (GLDPC) code is a class of codes, where single parity check nodes in a conventional low-density parity-check (LDPC) code are replaced by linear codes with higher parity check constraints. In this…
Subspace codes are the $q$-analog of binary block codes in the Hamming metric. Here the codewords are vector spaces over a finite field. They have e.g. applications in random linear network coding, distributed storage, and cryptography. In…
We derive fundamental bounds for general quantum metrological models involving both temporal or spatial correlations (mathematically described by quantum combs), which may be effectively computed in the limit of a large number of probes or…
The use of partial geometries to construct parity-check matrices for LDPC codes has resulted in the design of successful codes with a probability of error close to the Shannon capacity at bit error rates down to $10^{-15}$. Such…
This paper concerns non-overlapping codes, block codes motivated by synchronisation and DNA-based storage applications. Most existing constructions of these codes do not account for the restrictions posed by the physical properties of…
The persistent homology pipeline includes the reduction of a, so-called, boundary matrix. We extend the work of Bauer et al. (2014) and Chen et al. (2011) where they show how to use dependencies in the boundary matrix to adapt the reduction…
We provide evidence for the existence of non-trivial unitary conformal boundary conditions for a three-dimensional free scalar field, which can be obtained via a coupling to the m'th unitary diagonal minimal model. For large m we can…
Constrained coding plays a key role in optimizing performance and mitigating errors in applications such as storage and communication, where specific constraints on codewords are required. While non-parametric constraints have been…
Present work presents a code written in the very simple programming language MATLAB, for three dimensional linear elastostatics, using constant boundary elements. The code, in full or in part, is not a translation or a copy of any of the…
We explore the consequences of layering a Lambek proof system over an arbitrary (constraint) logic. A simple model-theoretic semantics for our hybrid language is provided for which a particularly simple combination of Lambek's and the proof…
A Waveguide Port Boundary Condition (WPBC) based on the restriction of the approximation space is presented in the context of Finite Element Analysis. As well as reducing the computational domain in the same manner as the traditional WPBC,…
Low-depth parity check (LDPC) codes are a paradigm of error correction that allow for spatially non-local interactions between (qu)bits, while still enforcing that each (qu)bit interacts only with finitely many others. On expander graphs,…
Given a compact basic semi-algebraic set we provide a numerical scheme to approximate as closely as desired, any finite number of moments of the Hausdorff measure on the boundary of this set. This also allows one to approximate interesting…
We prove partial and full boundary regularity for manifold constrained $p(x)$-harmonic maps.
Separating codes have their applications in collusion-secure fingerprinting for generic digital data, while they are also related to the other structures including hash family, intersection code and group testing. In this paper we study…
This paper is devoted to prove the exact controllability of a system of N one-dimensional coupled wave equations when the control is exerted on a part of the boundary by means of one control. We consider the case where the coupling matrix A…