相关论文: On two variations of identifying codes
Codes are crucial in many areas of applications. Different types of codes are designed to meet specific needs, which makes them more effective and useful. Linear codes are extensively used in data storage systems. Identifying codes are…
The Identifying Code (IC) problem seeks a vertex subset whose intersection with every vertex's closed neighborhood is unique, enabling fault detection in multiprocessor systems and practical uses in identity verification, environmental…
Sum-rank codes are an important class of codes which can be utilized for linear network coding, space-time coding and distributed storage. They can not only reduce the size of network alphabet but also detect and correct more errors. Based…
A Code loop on a binary linear code that is doubly even with a factor set is shown to be a central loop, conjugacy closed loop, Burn loop and extra loop. General forms of the identities that define the factor set of a code are deduced.
Binary linear [n,k] codes that are proper for error detection are known for many combinations of n and k. For the remaining combinations, existence of proper codes is conjectured. In this paper, a particular class of [n,k] codes is studied…
Linear codes have diverse applications in secret sharing schemes, secure two-party computation, association schemes, strongly regular graphs, authentication codes and communication. There are a large number of linear codes with few weights…
Zipper codes are a framework for describing spatially-coupled product-like codes. Many well-known codes, such as staircase codes and braided block codes, are subsumed into this framework. New types of codes such as tiled diagonal and…
A red-white coloring of a nontrivial connected graph $G$ is an assignment of red and white colors to the vertices of~$G$. Associated with each vertex $v$ of $G$ of diameter $d$ is a $d$-vector, called the code of $v$, whose $i$th coordinate…
Quantum low-density parity-check codes are promising candidates for quantum error correcting codes as they might offer more resource-efficient alternatives to surface code architectures. In particular, bivariate bicycle codes have recently…
We investigate weakly constrained codes, in which specific patterns occur with prescribed frequencies rather than being strictly forbidden as in conventional constrained coding. We propose a capacity-achieving construction of a weakly…
An unconventional encoding scheme called concurrent coding, has recently been demonstrated and shown to offer interesting features and benefits in comparison to conventional techniques, e.g. robustness against burst errors and improved…
We construct error correcting codes for jointly transmitting a finite set of independent messages to an 'informed receiver' which has prior knowledge of the values of some subset of the messages as side information. The transmitter is…
As a generalization of cyclic codes, quasi-cyclic (QC) codes contain many good linear codes. But quasi-cyclic codes studied so far are mainly limited to one generator (1-generator) QC codes. In this correspondence, 2-generator and…
We present a new family of quantum low-density parity-check codes, which we call radial codes, obtained from the lifted product of a specific subset of classical quasi-cyclic codes. The codes are defined using a pair of integers $(r,s)$ and…
Quantum error correction (QEC) codes are traditionally defined and searched for without specifying the manner in which its syndrome extraction circuits are executed using elementary gates and measurements. We show how morphing circuits…
We introduce a new family of codes, termed weighted superimposed codes (WSCs). This family generalizes the class of Euclidean superimposed codes (ESCs), used in multiuser identification systems. WSCs allow for discriminating all bounded,…
In this work we introduce two code families, which we call the heavy hexagon code and heavy square code. Both code families are implemented by assigning physical data and ancilla qubits to both vertices and edges of low degree graphs. Such…
Function-correcting codes are an innovative class of codes that are designed to protect a function evaluation of the data against errors or corruptions. Due to its usefulness in machine learning applications and archival data storage, where…
The concept of identifying codes was introduced by Karpovsky, Chakrabarty and Levitin in 1998. The identifying codes can be applied, for example, to sensor networks. In this paper, we consider as sensors the set Z^2 where one sensor can…
Subspace codes were introduced by K\"otter and Kschischang for error control in random linear network coding. In this paper, a layered type of subspace codes is considered, which can be viewed as a superposition of multiple component…