Results 11 to 20 of about 4,588 (252)
Multidimensional Quasi-Cyclic and Convolutional Codes [PDF]
IEEE Transactions on Information Theory, 2016 We introduce multidimensional analogues of quasi-cyclic (QC) codes and study their algebraic structure. We demonstrate a concatenated structure for multidimensional QC codes and use this to prove that this class of codes is asymptotically good. We also relate the new family of codes to convolutional codes.
Cem Güneri, Buket Özkaya
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Моделирование и анализ информационных систем, 2023 The development of fast algorithms for key generation, encryption and decryption not only increases the efficiency of related operations. Such fast algorithms, for example, for asymmetric cryptosystems on quasi-cyclic codes, make it possible to ...
Andrey N. Sushko +4 more
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On quasi-cyclic subspace codes
CoRR, 2016 Construction of subspace codes with good parameters is one of the most important problems in random network coding. In this paper we present first a generalization of the concept of cyclic subspaces codes and further we show that the usual methods for constructing cyclic subspace codes over finite fields works for m-quasi cyclic codes, namely the ...
Ismael Gutiérrez, Ivan Molina
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Quantum Quasi-Cyclic LDPC Codes [PDF]
2007 IEEE International Symposium on Information Theory, 2007 In this paper, a construction of a pair of "regular" quasi-cyclic LDPC codes as ingredient codes for a quantum error-correcting code is proposed. That is, we find quantum regular LDPC codes with various weight distributions. Furthermore our proposed codes have lots of variations for length, code rate. These codes are obtained by a descrete mathematical
Manabu Hagiwara, Hideki Imai
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Finite Fields and Their Applications, 2013 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Hongxi Tong, Ding Yang
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Quasi-Cyclic Codes Via Unfolded Cyclic Codes and Their Reversibility
IEEE Access, 2019 The finite field $\mathbb {F}_{q^\ell }$ of $q^\ell $ elements contains $\mathbb {F}_{q}$ as a subfield. If $\theta \in \mathbb {F}_{q^\ell }$ is of degree $\ell $ over $\mathbb {F}_{q}$ , it can be used to unfold elements of $\mathbb {F}_{q^\
Ramy Taki Eldin, Hajime Matsui
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Discrete Applied Mathematics, 2008 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Anne Desideri Bracco +2 more
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Decomposing Quasi-Cyclic Codes
Electronic Notes in Discrete Mathematics, 2001 Abstract A new algebraic approach to quasi-cyclic codes is introduced. Technical tools include the Chinese Remainder Theorem, the Discrete Fourier Transform, Chain rings. The main results are a characterization of self-dual quasi-cyclic codes, a trace representation that generalizes that of cyclic codes, and an interpretation of the squaring and ...
San Ling, Patrick Solé
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On the Construction of Skew Quasi-Cyclic Codes [PDF]
IEEE Transactions on Information Theory, 2010 In this paper we study a special type of quasi-cyclic (QC) codes called skew QC codes. This set of codes is constructed using a non-commutative ring called the skew polynomial rings $F[x;θ]$. After a brief description of the skew polynomial ring $F[x;θ]$ it is shown that skew QC codes are left submodules of the ring $R_{s}^{l}=(F[x;θ]/(x^{s}-1))^{l ...
Taher Abualrub +3 more
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Cyclic and Quasi-Cyclic DNA Codes
CoRR, 2021 draft, 16 ...
Adel Alahmadi +4 more
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