Results 11 to 20 of about 5,134,174 (310)
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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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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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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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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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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The minimum linear locality of linear codes
CoRR, 2021 Locally recoverable codes (LRCs) were proposed for the recovery of data in distributed and cloud storage systems about nine years ago. A lot of progress on the study of LRCs has been made by now. However, there is a lack of general theory on the minimum linear locality of linear codes.
Pan Tan +3 more
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Abstract Interpretation of Microcontroller Code: Intervals meet Congruences [PDF]
, 2013 Bitwise instructions, loops and indirect data access present challenges to the verification of microcontroller programs. In particular, since registers are often memory mapped, it is necessary to show that an indirect store operation does not accidently ...
Brauer, Jorg +2 more
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On Some Families of Codes Related to the Even Linear Codes Meeting the Grey–Rankin Bound
Mathematics, 2022 Bounds for the parameters of codes are very important in coding theory. The Grey–Rankin bound refers to the cardinality of a self-complementary binary code. Codes meeting this bound are associated with families of two-weight codes and other combinatorial
Iliya Bouyukliev +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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