Results 251 to 260 of about 4,270,277 (317)
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, 2017
In this chapter, we describe self-dual codes over Frobenius rings. We give constructions of self-dual codes over any Frobenius ring. We describe connections to unimodular lattices, binary self-dual codes and to designs. We also describe linear complementary dual codes and make a new definition of a broad generalization encompassing both self-dual and ...
S. Dougherty
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In this chapter, we describe self-dual codes over Frobenius rings. We give constructions of self-dual codes over any Frobenius ring. We describe connections to unimodular lattices, binary self-dual codes and to designs. We also describe linear complementary dual codes and make a new definition of a broad generalization encompassing both self-dual and ...
S. Dougherty
semanticscholar +3 more sources
The Dual Codes of Several Classes of BCH Codes
IEEE Transactions on Information Theory, 2021As a special subclass of cyclic codes, BCH codes have wide applications in communication and storage systems. A BCH code of length $n$ over $\mathbb {F}_{q}$ is always relative to an $n$ -th primitive root of unity $\beta $ in an extension field ...
Binkai Gong, C. Ding, Chengju Li
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Quasi-cyclic complementary dual codes
Finite Fields and Their Applications, 2015 LCD codes are linear codes that intersect with their dual trivially. Quasi cyclic codes that are LCD are characterized and studied by using their concatenated structure. Some asymptotic results are derived. Hermitian LCD codes are introduced to that end and their cyclic subclass is characterized.
Cem Güneri, Buket Özkaya, P. Solé
semanticscholar +6 more sources
MDS or NMDS self-dual codes from twisted generalized Reed–Solomon codes
Designs, Codes and Cryptography, 2020Self-dual maximum distance separable codes (self-dual MDS codes) and self-dual near MDS (NMDS) codes are very important in coding theory and practice. Thus, it is interesting to construct self-dual MDS or self-dual NMDS codes.
Daitao Huang +3 more
semanticscholar +1 more source
A Unified Approach to Construct MDS Self-Dual Codes via Reed-Solomon Codes
IEEE Transactions on Information Theory, 2020MDS codes and self-dual codes are important families of classical codes in coding theory. Therefore, it is of interest to investigate MDS self-dual codes. The existence of MDS self-dual codes over finite field ${\mathbb F}_{q}$ is competely solved for
Aixian Zhang, K. Feng
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Explicit Constructions of MDS Self-Dual Codes
IEEE Transactions on Information Theory, 2020In this paper, we study self-dual codes over finite fields using tools from algebraic function fields in one variable. An algebraic geometry code of length $n$ is defined using two divisors $G$ and $D=P_{1}+\cdots +P_{n}$ .
Lin Sok
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SIAM Journal on Discrete Mathematics, 1994
Summary: The authors present a construction of binary self-dual codes from Eulerian graphs and establish that the code will be indecomposable if and only if the vertices of degree 2 are not a cutset of the graph. The construction is used to establish that every finite group is isomorphic to the automorphism group of some self-dual code.
Babai, L., Oral, H., Phelps, K. T.
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Summary: The authors present a construction of binary self-dual codes from Eulerian graphs and establish that the code will be indecomposable if and only if the vertices of degree 2 are not a cutset of the graph. The construction is used to establish that every finite group is isomorphic to the automorphism group of some self-dual code.
Babai, L., Oral, H., Phelps, K. T.
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Dual-coded compressive hyperspectral imaging
Optics Letters, 2014This Letter presents a new snapshot approach to hyperspectral imaging via dual-optical coding and compressive computational reconstruction. We demonstrate that two high-speed spatial light modulators, located conjugate to the image and spectral plane, respectively, can code the hyperspectral datacube into a single sensor image such that the high ...
Xing, Lin +3 more
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New Constructions of MDS Euclidean Self-Dual Codes From GRS Codes and Extended GRS Codes
IEEE Transactions on Information Theory, 2019In this paper, we consider the problem for which lengths a maximum distance separable (MDS) Euclidean self-dual code over $\mathbb {F}_{q}$ exists. This problem is completely solved for the case where $q$ is even. For $q$ is odd, some $q$ -ary MDS
Weijun Fang, Fang-Wei Fu
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2011 IEEE Global Telecommunications Conference - GLOBECOM 2011, 2011
Alamouti codes have been widely recognized for their full-diversity performance, while they provide a symbol rate of one with symbol-by-symbol decoding complexity. To decode an Alamouti code, the receiver requires the channel state information (CSI), while the transmitter operates blindly without CSI.
null Liangbin Li, H. Jafarkhani
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Alamouti codes have been widely recognized for their full-diversity performance, while they provide a symbol rate of one with symbol-by-symbol decoding complexity. To decode an Alamouti code, the receiver requires the channel state information (CSI), while the transmitter operates blindly without CSI.
null Liangbin Li, H. Jafarkhani
openaire +1 more source