Results 21 to 30 of about 2,796,806 (297)
Duality of generalized twisted Reed-Solomon codes and Hermitian self-dual MDS or NMDS codes [PDF]
Cryptography and Communications, 2022 Self-dual MDS and NMDS codes over finite fields are linear codes with significant combinatorial and cryptographic applications. In this paper, firstly, we investigate the duality properties of generalized twisted Reed-Solomon (abbreviated GTRS) codes in ...
Guanmin Guo +3 more
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New LCD MDS Codes of Non-Reed-Solomon Type [PDF]
IEEE Transactions on Information Theory, 2021 Both linear complementary dual (LCD) codes and maximum distance separable (MDS) codes have good algebraic structures, and they have interesting practical applications such as communication systems, data storage, quantum codes, and so on.
Yansheng Wu, J. Hyun, Yoonjin Lee
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Infinite families of MDS and almost MDS codes from BCH codes
CoRR, 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,
Haojie Xu +3 more
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Near-MDS Codes from Maximal Arcs in PG$(2, q)$ [PDF]
Finite Fields Their Appl., 2022 The singleton defect of an $[n,k,d]$ linear code ${\cal C}$ is defined as $s({\cal C})=n-k+1-d$. Codes with $S({\cal C})=0$ are called maximum distance separable (MDS) codes, and codes with $S(\cal C)=S(\cal C ^{\bot})=1$ are called near maximum distance
Li Xu, Cuiling Fan, Dongchun Han
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Strongly-MDS convolutional codes [PDF]
IEEE Transactions on Information Theory, 2006 33 ...
Heide Gluesing-Luerssen +2 more
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Generalized Concatenated Codes over Gaussian and Eisenstein Integers for Code-Based Cryptography
Cryptography, 2021 The code-based McEliece and Niederreiter cryptosystems are promising candidates for post-quantum public-key encryption. Recently, q-ary concatenated codes over Gaussian integers were proposed for the McEliece cryptosystem, together with the one-Mannheim ...
Johann-Philipp Thiers +1 more
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Improved Field Size Bounds for Higher Order MDS Codes [PDF]
International Symposium on Information Theory, 2022 Higher order MDS codes are an interesting generalization of MDS codes recently introduced by Brakensiek, Gopi and Makam (IEEE Trans. Inf. Theory 2022).
Joshua Brakensiek +2 more
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Application of Constacyclic Codes to Quantum MDS Codes [PDF]
IEEE Transactions on Information Theory, 2015 Quantum maximal-distance-separable (MDS) codes form an important class of quantum codes. To get $q$-ary quantum MDS codes, it suffices to find linear MDS codes $C$ over $\mathbb{F}_{q^2}$ satisfying $C^{\perp_H}\subseteq C$ by the Hermitian construction and the quantum Singleton bound. If $C^{\perp_{H}}\subseteq C$, we say that $C$ is a dual-containing
Bocong Chen, San Ling, Guanghui Zhang
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IEEE Access, 2020 Let p ≠ 3 be any prime. The structures of all λ-constacyclic codes of length 3ps over the finite commutative chain ring Fpm + uFpm (u2 = 0) are established in the term of their generator polynomials.
Hai Q. Dinh +2 more
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Constructions of near MDS codes which are optimal locally recoverable codes [PDF]
Finite Fields Their Appl., 2022 A linear code with parameters $[n,k,n-k]$ is said to be almost maximum distance separable (AMDS for short). An AMDS code whose dual is also AMDS is referred to as an near maximum distance separable (NMDS for short) code. NMDS codes have nice applications
Xiaoru Li, Ziling Heng
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