Results 1 to 10 of about 58,958 (79)
Reproducible families of codes and cryptographic applications
Journal of Mathematical Cryptology, 2021 Structured linear block codes such as cyclic, quasi-cyclic and quasi-dyadic codes have gained an increasing role in recent years both in the context of error control and in that of code-based cryptography.
Santini Paolo +2 more
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Lower Bound on the Minimum Distance of Single-Generator Quasi-Twisted Codes
Mathematics, 2023 We recall a classic lower bound on the minimum Hamming distance of constacyclic codes over finite fields, analogous to the well-known BCH bound for cyclic codes.
Adel Alahmadi +2 more
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Bias-tailored quantum LDPC codes [PDF]
Quantum, 2023 Bias-tailoring allows quantum error correction codes to exploit qubit noise asymmetry. Recently, it was shown that a modified form of the surface code, the XZZX code, exhibits considerably improved performance under biased noise.
Joschka Roffe +4 more
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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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Quasi-cyclic subcodes of cyclic codes [PDF]
, 2016 We completely characterize possible indices of quasi-cyclic subcodes in a cyclic code for a very broad class of cyclic codes. We present enumeration results for quasi-cyclic subcodes of a fixed index and show that the problem of enumeration is equivalent
Belfiore, Jean-Claude +2 more
core +3 more sources
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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From Skew-Cyclic Codes to Asymmetric Quantum Codes [PDF]
, 2010 We introduce an additive but not $\mathbb{F}_4$-linear map $S$ from $\mathbb{F}_4^{n}$ to $\mathbb{F}_4^{2n}$ and exhibit some of its interesting structural properties.
A. R. Calderbank +16 more
core +1 more source
Cyclic lowest density MDS array codes [PDF]
, 2009 Three new families of lowest density maximum-distance separable (MDS) array codes are constructed, which are cyclic or quasi-cyclic. In addition to their optimal redundancy (MDS) and optimal update complexity (lowest density), the symmetry offered by the
Bruck, Jehoshua, Cassuto, Yuval
core +4 more sources
Sensors, 2023 The traditional LDPC encoding and decoding system is characterized by low throughput and high resource consumption, making it unsuitable for use in cost-efficient, energy-saving sensor networks.
Yuxuan Sun +5 more
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, 2014 We introduce {\bf complementary information set codes} of higher-order. A binary linear code of length $tk$ and dimension $k$ is called a complementary information set code of order $t$ ($t$-CIS code for short) if it has $t$ pairwise disjoint information
Carlet, Claude +5 more
core +3 more sources