Results 31 to 40 of about 63,034 (284)
Infinite families of MDS and almost MDS codes from BCH codes
, 2023 In this paper, the sufficient and necessary condition for the minimum distance of the BCH codes over $\mathbb{F}_q$ with length $q+1$ and designed distance 3 to be 3 and 4 are provided. Let $d$ be the minimum distance of the BCH code $\mathcal{C}_{(q,q+1,3,h)}$. We prove that (1) for any $q$, $d=3$ if and only if $\gcd(2h+1,q+1)>1$; (2) for $q$ odd,
Xu, Haojie +3 more
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The polycyclic codes over the finite field $ \mathbb{F}_q $
AIMS MathematicsThis article extended the properties of the idempotent generator of cyclic codes to polycyclic codes over the finite field $ \mathbb{F}_q $. In addition, the check matrix of polycyclic codes was provided over $ \mathbb{F}_q $.
Wei Qi
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Access vs. Bandwidth in Codes for Storage [PDF]
, 2012 Maximum distance separable (MDS) codes are widely used in storage systems to protect against disk (node) failures. A node is said to have capacity $l$ over some field $\mathbb{F}$, if it can store that amount of symbols of the field.
Bruck, Jehoshua +2 more
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New MDS entanglement-assisted quantum codes from MDS Hermitian self-orthogonal codes
Designs, Codes and Cryptography, 2023 The intersection ${\bf C}\bigcap {\bf C}^{\perp_H}$ of a linear code ${\bf C} \subset {\bf F}_{q^2}$ and its Hermitian dual ${\bf C}^{\perp_H}$ is called the Hermitian hull of this code. A linear code ${\bf C} \subset {\bf F}_{q^2}$ satisfying ${\bf C} \subset {\bf C}^{\perp_H}$ is called Hermitian self-orthogonal.
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MDS coded caching with MRT and its optimization
ICT Express, 2019 In conventional maximum distance separable (MDS) coded caching systems, storage-efficient caching strategy which minimizes unnecessarily redundant data is believed to be optimal.
Gibum Kim, Hyuncheol Park, Wan Choi
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Two-layer Locally Repairable Codes for Distributed Storage Systems [PDF]
, 2014 In this paper, we propose locally repairable codes (LRCs) with optimal minimum distance for distributed storage systems (DSS). A two-layer encoding structure is employed to ensure data reconstruction and the designated repair locality.
Xie, Hongmei, Yan, Zhiyuan
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Filomat, 2019 Linear codes with complementary duals (LCD) have a great deal of significance amongst linear codes. Maximum distance separable (MDS) codes are also an important class of linear codes since they achieve the greatest error correcting and detecting capabilities for fixed length and dimension. The construction of linear codes that are both LCD and MDS is a
Sarı, Mustafa, Köroğlu, Mehmet Emin
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Data distribution strategy based on the X-RDP array codes
Tongxin xuebao, 2013 A data distribution strategy based on the X-RDP code was presented for correcting triple storage failures, which is an extension of the double-erasure-correcting RDP code.
Wu-nan WAN, Wang SUO, Yun CHEN, Tuo WANG
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Provable Security of SP Networks with Partial Non-Linear Layers
IACR Transactions on Symmetric Cryptology, 2021 Motivated by the recent trend towards low multiplicative complexity blockciphers (e.g., Zorro, CHES 2013; LowMC, EUROCRYPT 2015; HADES, EUROCRYPT 2020; MALICIOUS, CRYPTO 2020), we study their underlying structure partial SPNs, i.e., Substitution ...
Chun Guo +4 more
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