Results 21 to 30 of about 90,302 (257)
Transitive distance-regular graphs from linear groups $L(3,q)$, $q = 2,3,4,5$ [PDF]
Transactions on Combinatorics, 2020 In this paper we classify distance-regular graphs, including strongly regular graphs, admitting a transitive action of the linear groups $L(3,2)$, $L(3,3)$, $L(3,4)$ and $L(3,5)$ for which the rank of the permutation representation is at most 15.
Andrea Svob
doaj +1 more source
Codes as fractals and noncommutative spaces [PDF]
, 2011 We consider the CSS algorithm relating self-orthogonal classical linear codes to q-ary quantum stabilizer codes and we show that to such a pair of a classical and a quantum code one can associate geometric spaces constructed using methods from ...
Marcolli, Matilde, Perez, Christopher
core +3 more sources
Connections between Linear Complementary Dual Codes, Permanents and Geometry
Mathematics, 2023 Linear codes with complementary duals, or LCD codes, have recently been applied to side-channel and fault injection attack-resistant cryptographic countermeasures.
Adel N. Alahmadi +5 more
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Extending binary linear codes to self-orthogonal codes
, 2021 Kim et al. (2021) gave a method to embed a given binary $[n,k]$ code $\mathcal{C}$ $(k = 3, 4)$ into a self-orthogonal code of the shortest length which has the same dimension $k$ and minimum distance $d' \ge d(\mathcal{C})$. We extend this result by proposing a new method related to a special matrix, called the self-orthogonality matrix $SO_k ...
Kim, Jon-Lark, Choi, Whan-Hyuk
openaire +2 more sources
Entanglement-assisted quantum error-correcting codes over arbitrary finite fields [PDF]
, 2019 We prove that the known formulae for computing the optimal number of maximally entangled pairs required for entanglement-assisted quantum error-correcting codes (EAQECCs) over the binary field hold for codes over arbitrary finite fields as well. We also
Galindo, Carlos +3 more
core +5 more sources
Quantum Error Correction via Codes over GF(4) [PDF]
, 1996 The problem of finding quantum error-correcting codes is transformed into the problem of finding additive codes over the field GF(4) which are self-orthogonal with respect to a certain trace inner product.
Calderbank, A. R. +3 more
core +10 more sources
On a generalization of the pless symmetry codes [PDF]
, 1975 A class of matrices which are orthogonal over the reals and contain only the elements, 0, ± 1, is constructed. For certain parameters, these matrices are used to construct a class of self dual codes over GF(3). This class is shown to contain the class of
Blake, Ian F.
core +1 more source
New Binary Quantum Codes Derived From One-Generator Quasi-Cyclic Codes
IEEE Access, 2019 In this paper, we consider a family of one-generator quasi-cyclic (QC) codes and their applications in quantum codes construction. We give a sufficient condition for one-generator QC codes to be self-orthogonal with respect to the symplectic inner ...
Jingjie Lv, Ruihu Li, Junli Wang
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Duality of codes over non-unital rings of order six
AIMS MathematicsSome basic theory on the duality of codes over two non-unital rings of order $ 6 $, namely $ H_{23} $ and $ H_{32} $ is presented. For a code $ {{\mathcal C}} $ over these rings, there is an associated binary code $ {{\mathcal C}}_a $ and a ternary code $
Altaf Alshuhail +2 more
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Hermitian Rank Metric Codes and Duality
IEEE Access, 2021 In this paper we define and study rank metric codes endowed with a Hermitian form. We analyze the duality for $\mathbb {F}_{q^{2}}$ -linear matrix codes in the ambient space $(\mathbb {F}_{q^{2}})_{n,m}$ and for both $\mathbb {F}_{q^{2}}$ -additive ...
Javier De La Cruz +2 more
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