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The main result here is a characterisation of binary $2$-neighbour-transitive codes with minimum distance at least $5$ via their minimal subcodes, which are found to be generated by certain designs. The motivation for studying this class of…
The performance of an error correcting code is evaluated by its error probability, rate, and en/decoding complexity. The performance of a series of codes is evaluated by, as the block lengths approach infinity, whether their error…
LDPC codes constructed from permutation matrices have recently attracted the interest of many researchers. A crucial point when dealing with such codes is trying to avoid cycles of short length in the associated Tanner graph, i.e. obtaining…
The present paper mainly studies limits and constructions of insertion and deletion (insdel for short) codes. The paper can be divided into two parts. The first part focuses on various bounds, while the second part concentrates on…
In this paper, we present an optimal metric function on average, which leads to a significantly low decoding computation while maintaining the superiority of the polarization-adjusted convolutional (PAC) codes' error-correction performance.…
Subspace codes, and in particular cyclic subspace codes, have gained significant attention in recent years due to their applications in error correction for random network coding. In this paper, we introduce a new technique for constructing…
Similarity, or clone, detection has important applications in copyright violation, software theft, code search, and the detection of malicious components. There is now a good number of open source and proprietary clone detectors for…
Sparse regression codes (SPARCs) are a promising coding scheme that can approach the Shannon limit over Additive White Gaussian Noise (AWGN) channels. Previous works have proven the capacity-achieving property of SPARCs with Gaussian design…
The main motivation of this paper is to introduce the permutation Jensen-Shannon distance, a symbolic tool able to quantify the degree of similarity between two arbitrary time series. This quantifier results from the fusion of two concepts,…
Geodesic tracking on the projective line bundle $\R^2 \times P^1 $ has many uses, including the segmentation of objects in images. However, global tracking requires expensive distance map computations. We provide a practical solution to…
This paper introduces Claycode, a novel 2D scannable code designed for extensive stylization and deformation. Unlike traditional matrix-based codes (e.g., QR codes), Claycodes encode their message in a tree structure. During the encoding…
Reward hacking is a form of misalignment in which models overoptimize proxy rewards without genuinely solving the underlying task. Precisely measuring reward hacking occurrence remains challenging because true task rewards are often…
We introduce a binary embedding framework, called Proximity Preserving Code (PPC), which learns similarity and dissimilarity between data points to create a compact and affinity-preserving binary code. This code can be used to apply fast…
For a growing number of applications such as cellular, peer-to-peer, and sensor networks, efficient error-free transmission of data through a network is essential. Toward this end, K\"{o}tter and Kschischang propose the use of subspace…
We developed an algorithm that easily goes from one odd number to the next odd number in binary representation for the reduced forward Collatz map (Syracuse function). The algorithm indicates when an odd number can grow or shrink to the…
For several decades, much effort has been put into identifying classes of CNF formulas whose satisfiability can be decided in polynomial time. Classic results are the linear-time tractability of Horn formulas (Aspvall, Plass, and Tarjan,…
We first present a simple recursive algorithm that generates cyclic rotation Gray codes for stamp foldings and semi-meanders, where consecutive strings differ by a stamp rotation. These are the first known Gray codes for stamp foldings and…
Tensor codes are a generalisation of matrix codes. Such codes are defined as subspaces of order-r tensors for which the ambient space is endowed with the tensor-rank as a metric. A class of these codes was introduced by Roth, who also…
Sparse superposition codes, also called sparse regression codes (SPARCs), are a class of codes for efficient communication over the AWGN channel at rates approaching the channel capacity. In a standard SPARC, codewords are sparse linear…
A permutation-invariant quantum code on $N$ qudits is any subspace stabilized by the matrix representation of the symmetric group $S_N$ as permutation matrices that permute the underlying $N$ subsystems. When each subsystem is a complex…