Related papers: Maximally Extendable Product Codes are Good Coboun…
We propose a modified iterative bounded distance decoding of product codes. The proposed algorithm is based on exchanging hard messages iteratively and exploiting channel reliabilities to make hard decisions at each iteration. Performance…
In this work, we study the sample complexity of two variants of product testing when restricted to single-copy measurements. In particular, we consider both bipartite product testing (i.e., does there exist at least one non-trivial cut…
The surface code is a quantum error-correcting code for one logical qubit, protected by spatially localized parity checks in two dimensions. Due to fundamental constraints from spatial locality, storing more logical qubits requires either…
In this paper, we present a new construction of asymmetric quantum codes (AQCs) by combining classical concatenated codes (CCs) with tensor product codes (TPCs), called asymmetric quantum concatenated and tensor product codes (AQCTPCs)…
We give a construction of Quantum Low-Density Parity Check (QLDPC) codes with near-optimal rate-distance tradeoff and efficient list decoding up to the Johnson bound in polynomial time. Previous constructions of list decodable good distance…
We study sheaves on posets, showing that cosystolic expansion of such sheaves can be derived from local expansion conditions of the sheaf and the poset (typically a high dimensional expander). When the poset at hand is a cell complex, a…
Locally repairable codes have become a key instrument in large-scale distributed storage systems. This paper focuses on the construction of locally repairable codes with $(r,\delta)$-locality that achieve the equality in the Singleton-type…
A locally testable code is an error-correcting code that admits very efficient probabilistic tests of membership. Tensor codes provide a simple family of combinatorial constructions of locally testable codes that generalize the family of…
Quantum expanders are a quantum analogue of expanders, and k-tensor product expanders are a generalisation to graphs that randomise k correlated walkers. Here we give an efficient construction of constant-degree, constant-gap quantum…
Quantum low-density parity-check (qLDPC) codes can be implemented by measuring only low-weight checks, making them compatible with noisy quantum hardware and central to the quest to build noise-resilient quantum computers. A fundamental…
Geometrically local quantum codes, comprised of qubits and checks embedded in $\mathbb{R}^D$ with local check operators, have been a subject of significant interest. A key challenge is identifying the optimal code construction that…
We consider the problem of determining the expected dimension of the star product of two uniformly random linear codes that are not necessarily of the same dimension. We achieve this by establishing a correspondence between the star product…
Locally repairable codes (LRCs) are a class of codes designed for the local correction of erasures. They have received considerable attention in recent years due to their applications in distributed storage. Most existing results on LRCs do…
We introduce the concept of quantum tensor product expanders. These are expanders that act on several copies of a given system, where the Kraus operators are tensor products of the Kraus operator on a single system. We begin with the…
Generalized product codes (GPCs) are extensions of product codes (PCs) where coded bits are protected by two component codes but not necessarily arranged in a rectangular array. It has recently been shown that there exists a large class of…
We study ensembles of codes on graphs (generalized low-density parity-check, or LDPC codes) constructed from random graphs and fixed local constrained codes, and their extension to codes on hypergraphs. It is known that the average minimum…
In this work, we explore the notions unextendible product basis and uncompletability for operators which remain positive under partial transpose. Then, we analyze their connections to the ensembles which are many-copy indistinguishable…
We initiate the probabilistic analysis of linear programming (LP) decoding of low-density parity-check (LDPC) codes. Specifically, we show that for a random LDPC code ensemble, the linear programming decoder of Feldman et al. succeeds in…
Several authors have proposed spatially-coupled (or convolutional-like) variants of product codes (PCs). In this paper, we focus on a parametrized family of generalized PCs that recovers some of these codes (e.g., staircase and block-wise…
Let $R$ be a commutative ring with identity. The paper studies the problem of self-orthogonality and self-duality matrix-product codes (MPCs) over $R$. Some methods as well as special matrices are introduced for the construction of such…