Related papers: On two variations of identifying codes
The outsourced manufacturing of integrated circuits has increased the risk of intellectual property theft. In response, logic locking techniques have been developed for protecting designs by adding programmable elements to the circuit.…
Codes for storage systems aim to minimize the repair locality, which is the number of disks (or nodes) that participate in the repair of a single failed disk. Simultaneously, the code must sustain a high rate, operate on a small finite…
The code that combines channel estimation and error protection has received general attention recently, and has been considered a promising methodology to compensate multi-path fading effect. It has been shown by simulations that such code…
Quantum error correcting codes protect quantum computation from errors caused by decoherence and other noise. Here we study the problem of designing logical operations for quantum error correcting codes. We present an automated procedure…
In 1969 J. Verhoeff provided the first examples of a decimal error detecting code using a single check digit to provide protection against all single, transposition and adjacent twin errors. The three codes he presented are length 3-digit…
Quantum error-correcting codes aim to protect information in quantum systems to enable fault-tolerant quantum computations. The most prevalent method, stabilizer codes, has been well developed for many varieties of systems, however, largely…
Non-binary low-density parity-check (LDPC) codes have some advantages over their binary counterparts, but unfortunately their decoding complexity is a significant challenge. The iterative hard- and soft-reliability based majority-logic…
Binary code similarity approaches compare two or more pieces of binary code to identify their similarities and differences. The ability to compare binary code enables many real-world applications on scenarios where source code may not be…
We consider identifying codes in binary Hamming spaces F^n, i.e., in binary hypercubes. The concept of identifying codes was introduced by Karpovsky, Chakrabarty and Levitin in 1998. Currently, the subject forms a topic of its own with…
An identifying code in a graph is a set of vertices which intersects all the symmetric differences between pairs of neighbourhoods of vertices. Not all graphs have identifying codes; those that do are referred to as twin-free. In this…
We construct new families of multi-error-correcting quantum codes for the amplitude damping channel. Our key observation is that, with proper encoding, two uses of the amplitude damping channel simulate a quantum erasure channel. This…
High voltage power transformers are one of the most critical equipments in the electric power grid. A sudden failure of a power transformer can significantly disrupt bulk power delivery. Before a transformer reaches its critical failure…
The problem of identifying whether the family of cyclic codes is asymptotically good or not is a long-standing open problem in the field of coding theory. It is known in the literature that some families of cyclic codes such as BCH codes…
List recovery is a fundamental task for error-correcting codes, vastly generalizing unique decoding from worst-case errors and list decoding. Briefly, one is given ''soft information'' in the form of input lists S_1,...,S_n of bounded size,…
An efficient algorithm for classification of binary self-dual codes is presented. As an application, a complete classification of the self-dual codes of length 38 is given.
In Ref. [1], Bravyi et al. found examples of Bivariate Bicycle (BB) codes with similar logical performance to the surface code but with an improved encoding rate. In this work, we generalize a novel parity-check circuit design principle…
We introduce two notions of discrepancy between binary vectors, which are not metric functions in general but nonetheless capture the mathematical structure of the binary asymmetric channel. In turn, these lead to two new fundamental…
The design of block codes for short information blocks (e.g., a thousand or less information bits) is an open research problem that is gaining relevance thanks to emerging applications in wireless communication networks. In this paper, we…
Alternative codes, an extension of the notion of ordinary codes, have been first introduced and considered by P. T. Huy et al. in 2004. As seen below, every alternative code, in its turn, defines an ordinary code. Such codes are called…
Flag verification techniques are useful in quantum error correction for detecting critical faults. Here we present an application of flag verification techniques to improving post-selected performance of near-term algorithms. We extend the…