Related papers: Function-Correcting Codes with Homogeneous Distanc…
The high overhead of fault-tolerant measurement sequences (FTMSs) poses a major challenge for implementing quantum stabilizer codes. Here, we address this problem by constructing efficient FTMSs for the class of quantum Hamming codes…
Compression-based similarity measures are effectively employed in applications on diverse data types with a basically parameter-free approach. Nevertheless, there are problems in applying these techniques to medium-to-large datasets which…
Linear error-correcting codes form the mathematical backbone of modern digital communication and storage systems, but identifying champion linear codes (linear codes achieving or exceeding the best known minimum Hamming distance) remains…
Quantum error correction plays a prominent role in the realization of quantum computation, and quantum low-density parity-check (qLDPC) codes are believed to be practically useful stabilizer codes. While qLDPC codes are defined to have…
In \cite{shi2022few-weight}, Shi and Li studied $\mathcal{C}_D$-codes over the ring $\mathcal{R}:=\mathbb{F}_2[x,y]/\langle x^2, y^2, xy-yx\rangle$ and their binary Gray images, where $D$ is derived using certain simplicial complexes. We…
A covering code is a set of codewords with the property that the union of balls, suitably defined, around these codewords covers an entire space. Generally, the goal is to find the covering code with the minimum size codebook. While most…
HYPERDIRE is a project devoted to the creation of a set of Mathematica based programs for the differential reduction of hypergeometric functions. The current version includes two parts: the first one, FdFunction, for manipulations with…
Constant-dimension codes have recently received attention due to their significance to error control in noncoherent random linear network coding. What the maximal cardinality of any constant-dimension code with finite dimension and minimum…
We introduce the class of partition-balanced families of codes, and show how to exploit their combinatorial invariants to obtain upper and lower bounds on the number of codes that have a prescribed property. In particular, we derive precise…
Coherent network error correction is the error-control problem in network coding with the knowledge of the network codes at the source and sink nodes. With respect to a given set of local encoding kernels defining a linear network code, we…
We consider a new family of codes, termed asymmetric Lee distance codes, that arise in the design and implementation of DNA-based storage systems and systems with parallel string transmission protocols. The codewords are defined over a…
Single hidden layer feedforward neural networks can represent multivariate functions that are sums of ridge functions. These ridge functions are defined via an activation function and customizable weights. The paper deals with best…
A lower bound on the number of uncorrectable errors of weight half the minimum distance is derived for binary linear codes satisfying some condition. The condition is satisfied by some primitive BCH codes, extended primitive BCH codes,…
Several new applications and a number of new mathematical techniques have increased the research on error-correcting codes in the Lee metric in the last decade. In this work we consider several coding problems and constructions of…
In this work, we introduce convolutional codes for network-error correction in the context of coherent network coding. We give a construction of convolutional codes that correct a given set of error patterns, as long as consecutive errors…
Linear complementary pairs (LCPs) of codes have been studied since they were introduced in the context of discussing mitigation measures against possible hardware attacks to integrated circuits. In this situation, the security parameters…
Insertion-deletion codes (insdel codes for short) are used for correcting synchronization errors in communications, and in other many interesting fields such as DNA storage, date analysis, race-track memory error correction and language…
This paper introduces a checksum algorithm that provides a new point in the performance/complexity/effectiveness checksum tradeoff space. It has better fault detection properties than single-sum and dual-sum modular addition checksums. It…
Lookup table decoding is fast and distance-preserving, making it attractive for near-term quantum computer architectures with small-distance quantum error-correcting codes. In this work, we develop several optimization tools that can…
This paper presents the generalization of weighted distances to modules and their computation through the chamfer algorithm on general point lattices. The first part is dedicated to formalization of definitions and properties (distance,…