Results 11 to 20 of about 115,969 (299)
How Many Weights Can a Quasi-Cyclic Code Have?
IEEE Transactions on Information Theory, 2020 We investigate the largest number of nonzero weights of quasi-cyclic codes. In particular, we focus on the function $\Gamma _{Q}(n,\ell,k,q)$ , that is defined to be the largest number of nonzero weights a quasi-cyclic code of index $\gcd (\ell,n ...
Minjia Shi, Alessandro Neri, P. Solé
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New Binary Quantum Codes Derived From One-Generator Quasi-Cyclic Codes
IEEE Access, 2019 In this paper, we consider a family of one-generator quasi-cyclic (QC) codes and their applications in quantum codes construction. We give a sufficient condition for one-generator QC codes to be self-orthogonal with respect to the symplectic inner ...
Jingjie Lv, Ruihu Li, Junli Wang
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On Reversibility and Self-Duality for Some Classes of Quasi-Cyclic Codes
IEEE Access, 2020 In this work, we study two classes of quasi-cyclic (QC) codes and examine how several properties can be combined into the codes of these classes. We start with the class of QC codes generated by diagonal generator polynomial matrices; a QC code in this ...
Ramy Taki Eldin, Hajime Matsui
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Efficient Encryption From Random Quasi-Cyclic Codes [PDF]
IEEE Transactions on Information Theory, 2016 We propose a framework for constructing efficient code-based encryption schemes that do not hide any structure in their public matrix. The framework is in the spirit of the schemes first proposed by Alekhnovich in 2003 and based on the difficulty of ...
C. Aguilar-Melchor +4 more
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Structure and performance of generalized quasi-cyclic codes [PDF]
Finite Fields and Their Applications, 2017 Generalized quasi-cyclic (GQC) codes form a natural generalization of quasi-cyclic (QC) codes. They are viewed here as mixed alphabet codes over a family of ring alphabets.
Cem Güneri +5 more
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Quantum Coding via Quasi-Cyclic Block Matrix
Entropy, 2023 An effective construction method for long-length quantum code has important applications in the field based on large-scale data. With the rapid development of quantum computing, how to construct this class of quantum coding has become one of the key ...
Yuan Li, Jin-Yang Li
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Efficient One-Time Signatures from Quasi-Cyclic Codes: A Full Treatment
Cryptography, 2018 The design of a practical code-based signature scheme is an open problem in post-quantum cryptography. This paper is the full version of a work appeared at SIN’18 as a short paper, which introduced a simple and efficient one-time secure signature ...
Edoardo Persichetti
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On Euclidean, Hermitian and symplectic quasi-cyclic complementary dual codes [PDF]
arXiv.org, 2023 Linear complementary dual codes (LCD) intersect trivially with their dual. In this paper, we develop a new characterization for LCD codes, which allows us to judge the complementary duality of linear codes from the codeword level.
Chaofeng Guan, Ruihu Li, Zhi Ma
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On the hull and complementarity of one generator quasi-cyclic codes and four-circulant codes [PDF]
Journal of Algebra and its Applications, 2023 We study one generator quasi-cyclic codes and four-circulant codes, which are also quasi-cyclic but have two generators. We state the hull dimensions for both classes of codes in terms of the polynomials in their generating elements.
Zohreh Aliabadi +2 more
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Automorphism Ensemble Decoding of Quasi-Cyclic LDPC Codes by Breaking Graph Symmetries [PDF]
IEEE Communications Letters, 2022 We consider automorphism ensemble decoding (AED) of quasi-cyclic (QC) low-density parity-check (LDPC) codes. Belief propagation (BP) decoding on the conventional factor graph is equivariant to the quasi-cyclic automorphisms and therefore prevents gains ...
Marvin Geiselhart +4 more
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