Related papers: Machine learning discovers new champion codes
We propose to use the concept of the Hamming bound to derive the optimal criteria for learning hash codes with a deep network. In particular, when the number of binary hash codes (typically the number of image categories) and code length…
This paper examines linear binary codes capable of correcting one or more errors. For the single-error-correcting case, it is shown that the Hamming bound is achieved by a constructive method, and an exact expression for the minimal…
The puncturing and shortening technique are two important approaches to constructing new linear codes from old ones. In the past 70 years, a lot of progress on the puncturing technique has been made, and many works on punctured linear codes…
The evaluation of the minimum distance of linear block codes remains an open problem in coding theory, and it is not easy to determine its true value by classical methods, for this reason the problem has been solved in the literature with…
We design a heuristic method, a genetic algorithm, for the computation of an upper bound of the minimum distance of a linear code over a finite field. By the use of the row reduced echelon form, we obtain a permutation encoding of the…
Linear codes play a central role in coding theory and have applications in several branches of mathematics. For error correction purposes the minimum Hamming distance should be as large as possible. Linear codes related to applications in…
The problem of coding for networks experiencing worst-case symbol errors is considered. We argue that this is a reasonable model for highly dynamic wireless network transmissions. We demonstrate that in this setup prior network…
Error control is significant to network coding, since when unchecked, errors greatly deteriorate the throughput gains of network coding and seriously undermine both reliability and security of data. Two families of codes, subspace and rank…
New lower bounds on the minimum average Hamming distance of binary codes are derived. The bounds are obtained using linear programming approach.
It has been widely observed that there exists a fundamental trade-off between the minimum (Hamming) distance properties and the iterative decoding convergence behavior of turbo-like codes. While capacity achieving code ensembles typically…
We examine an error-correcting coding framework in which each coded symbol is constrained to be a function of a fixed subset of the message symbols. With an eye toward distributed storage applications, we seek to design systematic codes…
Quantum error correction and the use of quantum error correction codes is likely to be essential for the realisation of practical quantum computing. Because the error models of quantum devices vary widely, quantum codes which are tailored…
Linear programming approaches have been applied to derive upper bounds on the size of classical codes and quantum codes. In this paper, we derive similar results for general quantum codes with entanglement assistance, including nonadditive…
The construction of optimal linear block error-correcting codes is not an easy problem, for this, many studies describe methods for generating good error correcting codes in terms of minimum distance. In a previous work, we have presented…
Finding the minimum distance of linear codes is an NP-hard problem. Traditionally, this computation has been addressed by means of the design of algorithms that find, by a clever exhaustive search, a linear combination of some generating…
The problem of error-control in random linear network coding is considered. A ``noncoherent'' or ``channel oblivious'' model is assumed where neither transmitter nor receiver is assumed to have knowledge of the channel transfer…
We consider network coding for networks experiencing worst-case bit-flip errors, and argue that this is a reasonable model for highly dynamic wireless network transmissions. We demonstrate that in this setup prior network error-correcting…
The design of large libraries of oligonucleotides having constant GC-content and satisfying Hamming distance constraints between oligonucleotides and their Watson-Crick complements is important in reducing hybridization errors in DNA…
Motivated by applications to distributed storage, Gopalan \textit{et al} recently introduced the interesting notion of information-symbol locality in a linear code. By this it is meant that each message symbol appears in a parity-check…
We present a powerful new loss function and training scheme for learning binary hash codes with any differentiable model and similarity function. Our loss function improves over prior methods by using log likelihood loss on top of an…