Two Families of BCH Codes and New Quantum Codes
Sign Up to like & getrecommendations! Published in 2019 at "International Journal of Theoretical Physics"
DOI: 10.1007/s10773-019-04120-9
Abstract: In this paper, two families of Hermitian dual-containing Bose-Chau- dhuri-Hocquenghem (BCH) codes with length n=a⋅q2+12$n=a\cdot \frac {q^{2}+ 1}{2}$ and n = b (q2 + 1) are studied, where odd a∣(q − 1) for odd prime power q and… read more here.
Keywords: new quantum; families bch; codes new; two families ... See more keywords
Constacyclic codes over the ring $${\mathbb {F}}_q+v{\mathbb {F}}_q+v^{2}{\mathbb {F}}_q$$Fq+vFq+v2Fq and their applications of constructing new non-binary quantum codes
Sign Up to like & getrecommendations! Published in 2018 at "Quantum Information Processing"
DOI: 10.1007/s11128-018-1898-6
Abstract: Let $$R={\mathbb {F}}_q+v{\mathbb {F}}_q+v^{2}{\mathbb {F}}_q$$R=Fq+vFq+v2Fq be a finite non-chain ring, where q is an odd prime power and $$v^3=v$$v3=v. In this paper, we propose two methods of constructing quantum codes from $$(\alpha +\beta v+\gamma v^{2})$$(α+βv+γv2)-constacyclic… read more here.
Keywords: mathbb vfq; quantum codes; mathbb mathbb; mathbb ... See more keywords
New optimal asymmetric quantum codes and quantum convolutional codes derived from constacyclic codes
Sign Up to like & getrecommendations! Published in 2019 at "Quantum Information Processing"
DOI: 10.1007/s11128-018-2156-7
Abstract: In this paper, some families of asymmetric quantum codes and quantum convolutional codes that satisfy the quantum Singleton bound are constructed by utilizing constacyclic codes with length $$n=\frac{q^2+1}{10h}$$n=q2+110h, where q is an odd prime power… read more here.
Keywords: quantum convolutional; convolutional codes; codes quantum; asymmetric quantum ... See more keywords
Nonbinary quantum codes from constacyclic codes over polynomial residue rings
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DOI: 10.1007/s11128-020-2584-z
Abstract: Let R be the polynomial residue ring $${\mathbb {F}}_{q^{2}}+u{\mathbb {F}}_{q^{2}}$$ F q 2 + u F q 2 , where $${\mathbb {F}}_{q^2}$$ F q 2 is the finite field with $$q^2$$ q 2 elements, q… read more here.
Keywords: quantum codes; mathbb mathbb; polynomial residue; mathbb ... See more keywords
Quantum codes from a new construction of self-orthogonal algebraic geometry codes
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DOI: 10.1007/s11128-020-2616-8
Abstract: We present new quantum codes with good parameters which are constructed from self-orthogonal algebraic geometry codes. Our method permits a wide class of curves to be used in the formation of these codes. These results… read more here.
Keywords: geometry codes; self orthogonal; algebraic geometry; quantum codes ... See more keywords
New classes of quantum codes on closed orientable surfaces
Sign Up to like & getrecommendations! Published in 2018 at "Cryptography and Communications"
DOI: 10.1007/s12095-018-0347-9
Abstract: In this paper we construct two classes of binary quantum error-correcting codes on closed orientable surfaces. These codes are derived from self-dual orientable embeddings of complete bipartite graphs and complete multipartite graphs on the corresponding… read more here.
Keywords: classes quantum; quantum codes; orientable surfaces; codes closed ... See more keywords
Decoding quantum errors with subspace expansions
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DOI: 10.1038/s41467-020-14341-w
Abstract: With rapid developments in quantum hardware comes a push towards the first practical applications. While fully fault-tolerant quantum computers are not yet realized, there may exist intermediate forms of error correction that enable practical applications.… read more here.
Keywords: quantum; post processing; quantum codes; decoding quantum ... See more keywords
Entanglement-assisted concatenated quantum codes
Sign Up to like & getrecommendations! Published in 2022 at "Proceedings of the National Academy of Sciences of the United States of America"
DOI: 10.1073/pnas.2202235119
Abstract: Significance Code concatenation that uses two or more short component codes is a significant method for designing powerful codes. Concatenated classical codes are not only asymptotically good in theory, but also have been widely used… read more here.
Keywords: entanglement assisted; concatenated quantum; entanglement; quantum codes ... See more keywords
Quantum homomorphic encryption from quantum codes
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DOI: 10.1103/physreva.98.042334
Abstract: The recent discovery of fully homomorphic classical encryption schemes has had a dramatic effect on the direction of modern cryptography. Such schemes, however, implicitly rely on the assumption that solving certain computation problems is intractable.… read more here.
Keywords: quantum; quantum homomorphic; quantum codes; encryption ... See more keywords
Single-Shot Decoding of Linear Rate LDPC Quantum Codes with High Performance
Sign Up to like & getrecommendations! Published in 2021 at "IEEE Transactions on Information Theory"
DOI: 10.1109/tit.2021.3122352
Abstract: We construct and analyze a family of low-density parity check (LDPC) quantum codes with a linear encoding rate, polynomial scaling distance and efficient decoding schemes. The code family is based on tessellations of closed, four-dimensional,… read more here.
Keywords: quantum codes; single shot; rate; ldpc quantum ... See more keywords