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Extended LP Bound for LCD codes and New Binary and Ternary LCD Codes
Applicable Algebra in Engineering, Communication and ComputingThe linear‐programming (LP) methodology proposed by Dougherty et al. originally formulated for binary LCD codes, is generalized herein to arbitrary $q$-ary settings. A unified LP bound is derived that subsumes and strengthens existing binary and ternary limits, yielding strictly tighter theoretical constraints.
Emre Karabakla, Buket Özkaya
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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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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.
Nouara 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.
Nouara Zoubir +3 more
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Computational and Applied Mathematics
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F. Rebaine, Kenza Guenda, T. A. Gulliver
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zbMATH Open Web Interface contents unavailable due to conflicting licenses.
F. Rebaine, Kenza Guenda, T. A. Gulliver
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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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On Hermitian LCD Generalized Gabidulin Codes
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, 2022Xubo Zhao +4 more
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Cyclic codes over a non-chain ring R, and their application to LCD codes
Discrete Mathematics, 2021Habibul Islam +2 more
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On Locality of Some Binary LCD Codes
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, 2023Ruipan Yang, Ruihu Li, Qiang Fu 0010
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New Quantum and LCD Codes Over the Finite Field of Odd Characteristic
International Journal of Theoretical Physics, 2021Mohammad Ashraf, Ghulam Mohammad
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New LCD MDS Codes of Non-Reed-Solomon Type
IEEE Transactions on Information Theory, 2021Yansheng Wu +2 more
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