Results 21 to 30 of about 7,931,944 (349)
Linear Codes from Two Weakly Regular Plateaued Balanced Functions
Entropy, 2023 Linear codes with a few weights have been extensively studied due to their wide applications in secret sharing schemes, strongly regular graphs, association schemes, and authentication codes.
Shudi Yang, Tonghui Zhang, Ping Li
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On the Grassmann graph of linear codes [PDF]
Finite Fields and Their Applications, 2021 Let $Γ(n,k)$ be the Grassmann graph formed by the $k$-dimensional subspaces of a vector space of dimension $n$ over a field $\mathbb F$ and, for $t\in \mathbb{N}\setminus \{0\}$, let $Δ_t(n,k)$ be the subgraph of $Γ(n,k)$ formed by the set of linear $[n,k]$-codes having minimum dual distance at least $t+1$. We show that if $|{\mathbb F}|\geq{n\choose t}
Cardinali, Ilaria +2 more
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Syndrome spectrums of error orbits in RS-codes
Системный анализ и прикладная информатика, 2020 This article is devoted to the research of the properties of syndromes of errors in Reed-Solomon codes. RS-codes are built on non-binary alphabets. So, unlike BCH-codes, RS-codes contain an extremely large variety of correctable errors.
V. A. Lipnitski, S. I. Semyonov
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Lee Weight and Generalized Lee Weight for Codes Over $Z_{2^n}$ [PDF]
Mathematics Interdisciplinary Research, 2023 Let $\mathbb{Z}_m$ be the ring of integers modulo $m$ in which $m=2^n$ for arbitrary $n$. In this paper, we will obtain a relationship between $wt_L(x), wt_L(y)$ and $wt_L(x+y)$ for any $x, y \in \mathbb{Z}_m$.
Farzaneh Farhang Baftani
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Estimating Channel Parameters from the Syndrome of a Linear Code [PDF]
IEEE Communications Letters, 2013 In this letter, we analyse the properties of a maximum likelihood channel estimator based on the syndrome of a linear code. For the two examples of a binary symmetric channel and a binary input additive white Gaussian noise channel, we derive expressions
G. Lechner, C. Pacher
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On the generalized Hamming weights of certain Reed–Muller-type codes
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2020 There is a nice combinatorial formula of P. Beelen and M. Datta for the r-th generalized Hamming weight of an a ne cartesian code. Using this combinatorial formula we give an easy to evaluate formula to compute the r-th generalized Hamming weight for a ...
González-Sarabia Manuel +2 more
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A New Code Based Signature Scheme for Blockchain Technology
Mathematics, 2023 Blockchain is a method of recording information that makes it not feasible for the system to be replaced, attacked, or manipulated. A blockchain is equipped with a notebook that copies and processes the various procedures across the network of computers ...
Adel Alahmadi +5 more
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Verus: Verifying Rust Programs using Linear Ghost Types [PDF]
Proc. ACM Program. Lang., 2023 The Rust programming language provides a powerful type system that checks linearity and borrowing, allowing code to safely manipulate memory without garbage collection and making Rust ideal for developing low-level, high-assurance systems.
Andrea Lattuada +8 more
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On the ideal associated to a linear code [PDF]
Advances in Mathematics of Communications, 2012 This article aims to explore the bridge between the algebraic structure of a linear code and the complete decoding process. To this end, we associate a specific binomial ideal $I_+(\mathcal C)$ to an arbitrary linear code.
Irene Marquez Corbella +2 more
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Fuzzy linear codes based on nested linear codes
Fuzzy Sets and Systems, 2023 In this paper, we describe a correspondence between a fuzzy linear code and a family of nested linear codes. We also describe the arithmetic of fuzzy linear codes. As a special class of nested linear codes, we consider a family of nested self-orthogonal codes.
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