Related papers: On decoding of a specific type of self-dual codes
Inspired by the recent advances in deep learning (DL), this work presents a deep neural network aided decoding algorithm for binary linear codes. Based on the concept of deep unfolding, we design a decoding network by unfolding the…
A complete classification of binary doubly even self-dual codes of length 40 is given. As a consequence, a classification of binary extremal self-dual codes of length 38 is also given.
A novel permutation decoding method for Reed-Muller codes is presented. The complexity and the error correction performance of the suggested permutation decoding approach are similar to that of the recursive lists decoder. It is…
The discovery of new quantum error-correcting codes that encode several logical qubits into relatively few physical qubits motivates the development of efficient and accurate methods of decoding these systems. Here, we adopt the…
This paper studies the problem of reconstructing binary matrices that are only accessible through few evaluations of their discrete X-rays. Such question is prominently motivated by the demand in material science for developing a tool for…
Hashing methods have been widely used for applications of large-scale image retrieval and classification. Non-deep hashing methods using handcrafted features have been significantly outperformed by deep hashing methods due to their better…
We initiate a study of locally decodable codes with randomized encoding. Standard locally decodable codes are error correcting codes with a deterministic encoding function and a randomized decoding function, such that any desired message…
Binary optimisation tasks are ubiquitous in areas ranging from logistics to cryptography. The exponential complexity of such problems means that the performance of traditional computational methods decreases rapidly with increasing problem…
In this paper we address the problem of decoding linearized Reed-Solomon (LRS) codes beyond their unique decoding radius. We analyze the complexity in order to evaluate if the considered problem is of cryptographic relevance, i.e., can be…
A new algorithm for efficient exact maximum likelihood decoding of polar codes (which may be CRC augmented), transmitted over the binary erasure channel, is presented. The algorithm applies a matrix triangulation process on a sparse polar…
We propose theoretical and empirical improvements for two-stage hashing methods. We first provide a theoretical analysis on the quality of the binary codes and show that, under mild assumptions, a residual learning scheme can construct…
In this work we present some results that allow to improve the decoding radius in solving polynomial linear systems with errors in the scenario where errors are additive and randomly distributed over a finite field. The decoding radius…
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…
We present a new fast Chase decoding algorithm for binary BCH codes. The new algorithm reduces the complexity in comparison to a recent fast Chase decoding algorithm for Reed--Solomon (RS) codes by the authors (IEEE Trans. IT, 2022), by…
Image hashing is a popular technique applied to large scale content-based visual retrieval due to its compact and efficient binary codes. Our work proposes a new end-to-end deep network architecture for supervised hashing which directly…
Vulnerability prediction is valuable in identifying security issues efficiently, even though it requires the source code of the target software system, which is a restrictive hypothesis. This paper presents an experimental study to predict…
Double polycirculant codes are introduced here as a generalization of double circulant codes. When the matrix of the polyshift is a companion matrix of a trinomial, we show that such a code is isodual, hence formally self-dual. Numerical…
We present the first known efficient decoding algorithm for correcting multiple insertion-deletion errors in Helberg codes and their non-binary generalizations, extending a known algorithm for correcting multiple deletion errors.
The minimum distance graph of a code has the codewords as vertices and edges exactly when the Hamming distance between two codewords equals the minimum distance of the code. A constructive proof for reconstructibility of an extended perfect…
A new permutation decoding approach for polar codes is presented. The complexity of the algorithm is similar to that of a successive cancellation list (SCL) decoder, while it can be implemented with the latency of a successive cancellation…