Results 1 to 10 of about 516,863 (164)
A consensus-based and readable extension of Linear Code for Reaction Rules (LiCoRR) [PDF]
Beilstein Journal of Organic Chemistry, 2020 Systems glycobiology aims to provide models and analysis tools that account for the biosynthesis, regulation, and interactions with glycoconjugates.
Benjamin P. Kellman +19 more
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An Extension of the Brouwer–Zimmermann Algorithm for Calculating the Minimum Weight of a Linear Code
Mathematics, 2021 A modification of the Brouwer–Zimmermann algorithm for calculating the minimum weight of a linear code over a finite field is presented. The aim was to reduce the number of codewords for consideration.
Stefka Bouyuklieva, Iliya Bouyukliev
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Triangular code: Near-optimal linear time fountain code
Digital Communications and Networks, 2023 In this paper, we propose Triangular Code (TC), a new class of fountain code with near-zero redundancy and linear encoding and decoding computational complexities of O(Lklogk), where k is the packet batch size and L is the packet data length.
Jalaluddin Qureshi, Chuan Heng Foh
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Error correction by Reed–Solomon codes using its automorphisms
Весці Нацыянальнай акадэміі навук Беларусі: Серыя фізіка-тэхнічных навук, 2021 The article explores the syndrome invariants of АГ-group of automorphisms of Reed–Solomon codes (RS-codes) that are a joint group of affine and cyclic permutations. The found real invariants are a set of norms of N Г-orbits that make up one or another АГ-
V. A. Lipnitsky, S. I. Semyonov
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Linear Computation Coding [PDF]
ICASSP 2021 - 2021 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 2021 We introduce the new concept of computation coding. Similar to how rate-distortion theory is concerned with the lossy compression of data, computation coding deals with the lossy computation of functions. Particularizing to linear functions, we present an algorithm to reduce the computational cost of multiplying an arbitrary given matrix with an ...
Ralf R. Müller +2 more
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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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Decoding Linear Codes over Chain Rings Given by Parity Check Matrices
Mathematics, 2021 We design a decoding algorithm for linear codes over finite chain rings given by their parity check matrices. It is assumed that decoding algorithms over the residue field are known at each degree of the adic decomposition.
José Gómez-Torrecillas +2 more
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The parameters of minimal linear codes [PDF]
Finite Fields and Their Applications, 2021 Let $k\leq n$ be two positive integers and $q$ a prime power. The basic question in minimal linear codes is to determine if there exists an $[n,k]_q$ minimal linear code. The first objective of this paper is to present a new sufficient and necessary condition for linear codes to be minimal.
Wei Lu 0022, Xia Wu 0002, Xiwang Cao
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Constacyclic Codes over Finite Chain Rings of Characteristic p
Axioms, 2021 Let R be a finite commutative chain ring of characteristic p with invariants p,r, and k. In this paper, we study λ-constacyclic codes of an arbitrary length N over R, where λ is a unit of R.
Sami Alabiad, Yousef Alkhamees
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Computer Classification of Linear Codes [PDF]
IEEE Transactions on Information Theory, 2021 We present algorithms for classification of linear codes over finite fields, based on canonical augmentation and on lattice point enumeration. We apply these algorithms to obtain classification results over fields with 2, 3 and 4 elements. We validate a correct implementation of the algorithms with known classification results from the literature ...
Iliya Bouyukliev +2 more
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