Results 31 to 40 of about 516,863 (164)

On the Covering Dimension of a Linear Code [PDF]

IEEE Transactions on Information Theory, 2016
The critical exponent of a matroid is one of the important parameters in matroid theory and is related to the Rota and Crapo's Critical Problem. This paper introduces the covering dimension of a linear code over a finite field, which is analogous to the critical exponent of a representable matroid.
Britz, T, Shiromoto, K
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Optimal Quaternary Hermitian LCD Codes

Entropy
Linear complementary dual (LCD) codes, which are a class of linear codes introduced by Massey, have been extensively studied in the literature recently.
Liangdong Lu, Ruihu Li, Yuezhen Ren
doaj   +1 more source

Linear intersecting codes

Discrete Mathematics, 1985
Several new and interesting properties of 'linear intersecting codes' are studied. The cyclic structure as well as the duals of such codes are also discussed. Relationships of such codes with many well-known codes in the binary and non-binary cases are established. Almost every study made in the paper is illustrated with an interesting example.
Gérard D. Cohen, Abraham Lempel
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Constant composition codes as subcodes of linear codes [PDF]

Journal of Applied Mathematics and Computing, 2019
13pages
Long Yu, Xiusheng Liu
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The extended codes of some linear codes

Finite Fields and Their Applications
The classical way of extending an $[n, k, d]$ linear code $\C$ is to add an overall parity-check coordinate to each codeword of the linear code $\C$. This extended code, denoted by $\overline{\C}(-\bone)$ and called the standardly extended code of $\C$, is a linear code with parameters $[n+1, k, \bar{d}]$, where $\bar{d}=d$ or $\bar{d}=d+1$.
Zhonghua Sun 0001, Cunsheng Ding, Tingfang Chen   +2 more
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CODING IN GRAPHS AND LINEAR ORDERINGS [PDF]

The Journal of Symbolic Logic, 2020
AbstractThere is a Turing computable embedding $\Phi $ of directed graphs $\mathcal {A}$ in undirected graphs (see [15]). Moreover, there is a fixed tuple of formulas that give a uniform effective interpretation; i.e., for all directed graphs $\mathcal {A}$ , these formulas interpret $\mathcal {A}$ in $\Phi (\mathcal {A})$ .
Julia F. Knight, Alexandra A. Soskova, Stefan V. Vatev   +2 more
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Additive Codes From Linear Codes

IEEE Transactions on Information Theory
We introduce two constructions of additive codes over finite fields. Both constructions start with a linear code over a field with $q$ elements and give additive codes over the field with $q^h$ elements whose minimum distance is demonstrably good.
Simeon Ball, Tabriz Popatia
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Linear transformations on codes

Discrete Mathematics, 2006
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
David G. Glynn, T. Aaron Gulliver, Manish K. Gupta 0004   +2 more
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Reversible Codes in Mat_n×s(Fq) Under NRT-Metric

IEEE Access
Reversible codes play an essential role in coding theory because of their structural symmetry and broad applications in error control, cryptography, and DNA computing.
Bodigiri Sai Gopinadh, Venkatrajam Marka
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Linear Codes Over a Non-Chain Ring and the MacWilliams Identities

IEEE Access, 2020
This paper is concerned with the linear codes over the non-chain ring R=F2[v]/〈v4-v〉. First, several weight enumerators over R are defined.
Tiantian Li, Rongsheng Wu, Juan Xu
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