Results 1 to 10 of about 290,159 (337)

Self-Dual Codes, Symmetric Matrices, and Eigenvectors [PDF]

IEEE Access, 2021
We introduce a consistent and efficient method to construct self-dual codes over $GF(q)$ using symmetric matrices and eigenvectors from a self-dual code over $GF(q)$ of smaller length where $q \equiv 1 \pmod 4$ . Using this method, which is called a
Jon-Lark Kim, Whan-Hyuk Choi
doaj   +3 more sources

Group rings, G-codes and constructions of self-dual and formally self-dual codes [PDF]

Designs, Codes, and Cryptography, 2017
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Alexander Tylyshchak, Rhian Taylor, Steven Dougherty   +2 more
exaly   +5 more sources

New Construction of Maximum Distance Separable (MDS) Self-Dual Codes over Finite Fields [PDF]

Entropy, 2019
Maximum distance separable (MDS) self-dual codes have useful properties due to their optimality with respect to the Singleton bound and its self-duality.
Aixian Zhang, Zhe Ji
doaj   +2 more sources

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, Altaf Alshuhail, Rowena Alma Betty, Lucky Galvez, Patrick Solé   +4 more
doaj   +2 more sources

Triorthogonal codes and self-dual codes

Quantum Information Processing
Triorthogonal matrices were introduced in quantum information theory in connection with distillation of magic states (Bravyi and Haah in Phys Rev A 86:052329, 2012).
Minjia Shi, Haodong Lu, Jon-Lark Kim, Patrick Solé   +3 more
semanticscholar   +3 more sources

Symplectic QSD, LCD, and ACD Codes over a Non-Commutative Non-Unitary Ring of Order Nine [PDF]

Entropy
We introduce quasi self-dual (QSD), linear complementary dual (LCD), and additive complementary dual (ACD) codes for the symplectic inner product over a non-commutative non-unitary ring of order 9. We establish connections with symplectic–self-orthogonal
Sarra Manseri, Patrick Solé, Adel Alahmadi, Widyan Basaffar   +3 more
doaj   +2 more sources

On McEliece-Type Cryptosystems Using Self-Dual Codes With Large Minimum Weight

IEEE Access, 2023
One of the Round 3 Finalists in the NIST post-quantum cryptography call is the Classic McEliece cryptosystem. Although it is one of the most secure cryptosystems, the large size of its public key remains a practical limitation. In this work, we propose a
Luca Mariot, Stjepan Picek, Radinka Yorgova   +2 more
doaj   +2 more sources

The Mass Formula for Self-Orthogonal and Self-Dual Codes over a Non-Unitary Non-Commutative Ring

Mathematics
In this paper, we derive a mass formula for the self-orthogonal codes and self-dual codes over a non-commutative non-unitary ring, namely, Ep=a,b|pa=pb=0,a2=a,b2=b,ab=a,ba=b, where a≠b and p is any odd prime.
Adel Alahmadi, Altaf Alshuhail, Rowena Alma Betty, Lucky Galvez, Patrick Solé   +4 more
doaj   +2 more sources

On Quasi-Cyclic Codes of Index 3 [PDF]

Entropy
Quasi-cyclic codes of index 3 over finite fields are studied. We give a classification of such codes. Their duals with respect to the Euclidean and Hermitian inner products are investigated.
Kanat Abdukhalikov, Rasha M. Shat
doaj   +2 more sources

New families of self-dual codes [PDF]

Designs, Codes and Cryptography, 2020
Recently, the author has constructed families of MDS Euclidean self-dual codes from genus zero algebraic geometry (AG) codes. In the present correspondence, more families of optimal Euclidean self-dual codes from AG codes are explored.
Lin Sok
semanticscholar   +5 more sources