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Designs, Codes and Cryptography
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de la Cruz, Javier, Willems, Wolfgang
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de la Cruz, Javier, Willems, Wolfgang
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Designs, Codes and Cryptography
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El Badry, Mohammed +2 more
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El Badry, Mohammed +2 more
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Discrete Mathematics, Algorithms and Applications
In this paper, we introduce several new construction techniques of linear complimentary dual (LCD) codes. First, we show that if a LCD code is fixed by a transitive automorphism group, then the punctured code is also LCD. We show that several important families such as anti-primitive BCH codes and extended Gabidulin codes are LCD.
N. Zoubir +3 more
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In this paper, we introduce several new construction techniques of linear complimentary dual (LCD) codes. First, we show that if a LCD code is fixed by a transitive automorphism group, then the punctured code is also LCD. We show that several important families such as anti-primitive BCH codes and extended Gabidulin codes are LCD.
N. Zoubir +3 more
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New LCD MDS codes constructed from generalized Reed–Solomon codes
Journal of Algebra and Its Applications, 2019Maximum distance separable codes with complementary duals (LCD MDS codes) are very important in coding theory and practice, and have attracted a lot of attention. In this paper, we focus on LCD MDS codes constructed from generalized Reed–Solomon (GRS) codes over a finite field with odd characteristic.
Shi, Xueying, Yue, Qin, Yang, Shudi
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Computational and Applied Mathematics
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F. Rebaine, K. Guenda, T. A. Gulliver
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F. Rebaine, K. Guenda, T. A. Gulliver
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Locally maximal recoverable codes and LMR-LCD codes
Designs, Codes and CryptographyThe paper introduces two new classes of \((r,\delta)\)-locally recoverable codes (LRCs), called locally maximal recoverable (LMR) codes and \(\lambda\)-maximally recoverable (MR) codes. These generalize the well-studied \((n,k,r,\delta,h)\)-MR codes, where \(h\) heavy (global) parities are added to \(k\) information symbols, then partitioned into ...
Rajendra Prasad Rajpurohit +2 more
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Some constructions of $l$-Galois LCD codes
Advances in Mathematics of CommunicationsLet \({\mathbb F}_q\) be the finite field with \(q = p^m\) elements. The Galois inner product is a generalization of Hermitian and Euclidean inner products. It's defined as \(a\ast_ l b= \sum\limits_{i=1}^{n}a_ib_i^{p^l},\) where \(0\leq l\leq m-1.\) Similarly, we can define the \(l\)-Galois dual code of \(C\) as \(C^{\bot_l}=\{a\in \mathbb{F}_q^n\vert
Yadav, Shikha +2 more
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Integrative oncology: Addressing the global challenges of cancer prevention and treatment
Ca-A Cancer Journal for Clinicians, 2022Jun J Mao,, Msce +2 more
exaly
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, 2018
Minjia SHI, Daitao HUANG
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Minjia SHI, Daitao HUANG
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Constructions of LCD subspace codes
The dual code of a code C is the orthogonal complement of C under the standard inner product (· , ·). Linear codes with complementary duals, or LCD codes, are linear codes whose intersection with their duals are trivial. LCD codes were introduced by Massey in [5] and have been widely applied in information protection, electronics and cryptography.Crnković, Dean, Švob, Andrea
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