Related papers: Identification Codes via Prime Numbers
The model of identification via channels, introduced by Ahlswede and Dueck, has attracted increasing attention in recent years. One such promising direction is message identification via channels, introduced by Ahlswede and Dueck. Unlike in…
This study introduces a decentralized approach to secure wireless communication using a cryptographic secret key generation algorithm among distributed nodes. The system model employs Gaussian prime numbers, ensuring the collaborative…
Prime numbers have fascinated mathematicians since antiquity, with ongoing efforts to uncover both their properties and ever-larger examples. While giant primes rarely aid cryptography, they find use in areas such as locally decodable…
The order statistics based list decoding techniques for linear binary block codes of small to medium block length are investigated. The construction of the list of the test error patterns is considered. The original order statistics…
In the case of ordinary identification coding, a code is devised to identify a single object among $N$ objects. But, in this paper, we consider an identification coding problem to identify $K$ objects at once among $N$ objects in the both…
We study medium access control layer random access under the assumption that the receiver can perform successive interference cancellation, without feedback. During recent years, a number of protocols with impressive error performance have…
Codes are crucial in many areas of applications. Different types of codes are designed to meet specific needs, which makes them more effective and useful. Linear codes are extensively used in data storage systems. Identifying codes are…
We give new constructions of two classes of algebraic code families which are efficiently list decodable with small output list size from a fraction $1-R-\epsilon$ of adversarial errors where $R$ is the rate of the code, for any desired…
A modified Lagrange Polynomial is introduced for polynomial extrapolation, which can be used to estimate the equally spaced values of a polynomial function. As an example of its application, this article presents a prime-generating…
Let $p$ be a prime number. Irreducible cyclic codes of length $p^2-1$ and dimension $2$ over the integers modulo $p^h$ are shown to have exactly two nonzero Hamming weights. The construction uses the Galois ring of characteristic $p^h$ and…
Homomorphic Encryption (HE) allows secure and privacy-protected computation on encrypted data without the need to decrypt it. Since Shor's algorithm rendered prime factorisation and discrete logarithm-based ciphers insecure with quantum…
Logarithmic gaps have been used in order to find a periodic component of the sequence of prime numbers, hidden by a random noise (stochastic or chaotic). The recovered period for the sequence of the first 10000 prime numbers is equal to…
We propose an unsupervised hashing method which aims to produce binary codes that preserve the ranking induced by a real-valued representation. Such compact hash codes enable the complete elimination of real-valued feature storage and allow…
This article proposes the use of pseudorandom decimal sequences that have gone through an additional random mapping for the design of cryptographic keys. These sequences are generated by starting with inverse prime expansions in base 3 and…
This paper introduces the notion of multiset codes as relevant to the problem of reliable information transmission over permutation channels. The motivation for studying permutation channels comes from the effect of out of order delivery of…
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…
We propose a new method for constructing small-bias spaces through a combination of Hermitian codes. For a class of parameters our multisets are much faster to construct than what can be achieved by use of the traditional algebraic…
Let $q$ be a prime power. This paper provides a new class of linear codes that arises from the action of the alternating group on $\mathbb F_q[x_1,\dots,x_m]$ combined with the ideas in (M. Datta and T. Johnsen, 2022). Compared with…
In this article we focus on the problem of channel decoding in presence of a-priori information. In particular, assuming that the a-priori information reliability is not perfectly estimated at the receiver, we derive a novel analytical…
The high computational cost of approaching the performance of Maximum-likelihood (ML) decoding has limited its practical use for decades. Because the complexity grows exponentially with the message length, researchers have spent years…