Results 1 to 10 of about 1,011,482 (281)
Minimal Linear Codes Constructed from Sunflowers [PDF]
Entropy, 2023 Sunflower in coding theory is a class of important subspace codes and can be used to construct linear codes. In this paper, we study the minimality of linear codes over Fq constructed from sunflowers of size s in all cases.
Xia Wu, Wei Lu
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Linear Codes from Two Weakly Regular Plateaued Balanced Functions [PDF]
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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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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SOME NEW CONSTRUCTIONS OF LINEAR CODES INCLUDING A WIDE FAMILY OF MDS CODES [PDF]
Journal of Algebraic Systems, 2020 Let $mathbb{Z}_p$ be the finite field of integers modulo $p$, where $p>3$ is a prime integer. This paper presents new constructions of linear codes over $mathbb{Z}_p$.
A. Rafieepour, M. Mazrooei
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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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A Unique Representation of Cyclic Codes over GR(pn,r)
Axioms, 2022 Let R be a Galois ring, GR(pn,r), of characteristic pn and of order pnr. In this article, we study cyclic codes of arbitrary length, N, over R. We use discrete Fourier transform (DFT) to determine a unique representation of cyclic codes of length, N, in ...
Sami Alabiad, Yousef Alkhamees
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Random linear codes in steganography [PDF]
Biuletyn Wojskowej Akademii Technicznej, 2016 Syndrome coding using linear codes is a technique that allows improvement in the steganographic algorithms parameters. The use of random linear codes gives a great flexibility in choosing the parameters of the linear code.
Kamil Kaczyński
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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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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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Some Results on Self-Complementary Linear Codes
Mathematics, 2023 Binary codes have a special place in coding theory since they are one of the most commonly used in practice. There are classes of codes specific only to the binary case. One such class is self-complementary codes.
Maria Pashinska-Gadzheva +2 more
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