Results 11 to 20 of about 90,302 (257)
Quantum codes from $ \sigma $-dual-containing constacyclic codes over $ \mathfrak{R}_{l, k} $
AIMS Mathematics, 2023 Let $ \mathfrak{R}_{l, k} = {\mathbb F}_{p^m}[u_1, u_2, \cdots, u_k]/ \langle u_{i}^{l} = u_{i}, u_iu_j = u_ju_i = 0 \rangle $, where $ p $ is a prime, $ l $ is a positive integer, $ (l-1)\mid(p-1) $ and $ 1\leq i, j\leq k $. First, we define a Gray map $
Xiying Zheng, Bo Kong, Yao Yu
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Self-Orthogonal Codes Constructed from Posets and Their Applications in Quantum Communication
Mathematics, 2020 It is an important issue to search for self-orthogonal codes for construction of quantum codes by CSS construction (Calderbank-Sho-Steane codes); in quantum error correction, CSS codes are a special type of stabilizer codes constructed from classical ...
Yansheng Wu, Yoonjin Lee
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Mass Formula for Self-Orthogonal and Self-Dual Codes over Non-Unital Rings of Order Four
Mathematics, 2023 We study the structure of self-orthogonal and self-dual codes over two non-unital rings of order four, namely, the commutative ring I=a,b|2a=2b=0,a2=b,ab=0 and the noncommutative ring E=a,b|2a=2b=0,a2=a,b2=b,ab=a,ba=b.
Adel Alahmadi +4 more
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Binary LCD Codes and Self-Orthogonal Codes via Simplicial Complexes [PDF]
IEEE Communications Letters, 2020 Due to some practical applications, linear complementary dual (LCD) codes and self-orthogonal codes have attracted wide attention in recent years. In this paper, we use simplicial complexes for construction of an infinite family of binary LCD codes and two infinite families of binary self-orthogonal codes.
Yansheng Wu, Yoonjin Lee
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On Reversibility and Self-Duality for Some Classes of Quasi-Cyclic Codes
IEEE Access, 2020 In this work, we study two classes of quasi-cyclic (QC) codes and examine how several properties can be combined into the codes of these classes. We start with the class of QC codes generated by diagonal generator polynomial matrices; a QC code in this ...
Ramy Taki Eldin, Hajime Matsui
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Self-orthogonal codes constructed from weakly self-orthogonal designs invariant under an action of $$M_{11}$$ [PDF]
Applicable Algebra in Engineering, Communication and Computing, 2021 In this paper we generalize the construction of binary self-orthogonal codes obtained from weakly self-orthogonal designs described by Tonchev in [12] in order to obtain self-orthogonal codes over an arbitrary field. We extend construction self-orthogonal codes from orbit matrices of self-orthogonal designs and weakly self-orthogonal 1-designs such ...
Mikulić Crnković, Vedrana +1 more
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Quasi self-dual codes over non-unital rings from three-class association schemes
AIMS Mathematics, 2023 Let $ E $ and $ I $ denote the two non-unital rings of order 4 in the notation of (Fine, 93) defined by generators and relations as $ E = \langle a, b \mid 2a = 2b = 0, a^2 = a, b^2 = b, ab = a, ba = b\rangle $ and $ I = \langle a, b \mid 2a = 2b = 0, a ...
Adel Alahmadi +2 more
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Algebraic geometric construction of a quantum stabilizer code [PDF]
, 2001 The stabilizer code is the most general algebraic construction of quantum error-correcting codes proposed so far. A stabilizer code can be constructed from a self-orthogonal subspace of a symplectic space over a finite field.
Matsumoto, Ryutaroh
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Transitive and self-dual codes attaining the Tsfasman-Vladut-Zink bound [PDF]
, 2005 A major problem in coding theory is the question of whether the class of cyclic codes is asymptotically good. In this correspondence-as a generalization of cyclic codes-the notion of transitive codes is introduced (see Definition 1.4 in Section I), and ...
Stichtenoth, Henning
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Extending self-orthogonal codes
TURKISH JOURNAL OF MATHEMATICS, 2019 Summary: In this short note we give an exact count for the number of self-dual codes over a finite field \(\mathbb{F}_q\) of odd characteristic containing a given self-orthogonal code. This generalizes an analogous result of \textit{F. J. MacWilliams} et al. [Discrete Math.
Bassa, Alp, Tutaş, Nesrin
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