New quantum codes from evaluation and matrix-product codes
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Publication:747973
DOI10.1016/j.ffa.2015.07.003zbMath1355.94093arXiv1406.0650OpenAlexW1903020140WikidataQ62582180 ScholiaQ62582180MaRDI QIDQ747973
Diego Ruano, Fernando Hernando, Carlos Galindo Pastor
Publication date: 19 October 2015
Published in: Finite Fields and their Applications (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1406.0650
Geometric methods (including applications of algebraic geometry) applied to coding theory (94B27) Quantum coding (general) (81P70)
Related Items (18)
On the generalization of the construction of quantum codes from Hermitian self-orthogonal codes ⋮ On the evaluation codes given by simple \(\delta \)-sequences ⋮ Matrix-Product Constructions for Hermitian Self-Orthogonal Codes ⋮ On the distance of stabilizer quantum codes from \(J\)-affine variety codes ⋮ On self-orthogonality and self-duality of matrix-product codes over commutative rings ⋮ New quantum codes from matrix-product codes over small fields ⋮ Construction of new quantum codes via Hermitian dual-containing matrix-product codes ⋮ Application of Euclidean sums of matrix-product codes to quantum codes ⋮ Hermitian dual-containing constacyclic codes over \(\mathbb{F}_{q^2}+v_1 \mathbb{F}_{q^2}+\cdots +v_r \mathbb{F}_{q^2}\) and new quantum codes ⋮ Several new families of MDS EAQECCs with much larger dimensions and related application to EACQCs ⋮ Matrix-product codes related to constacyclic codes and their applications to EAQEC codes ⋮ On new quantum codes from matrix product codes ⋮ The Metric Structure of Linear Codes ⋮ Matrix-product codes over commutative rings and constructions arising from \((\sigma,\delta)\)-codes ⋮ Stabilizer quantum codes from \(J\)-affine variety codes and a new Steane-like enlargement ⋮ New stabilizer codes from the construction of dual-containing matrix-product codes ⋮ The hulls of matrix-product codes over commutative rings and applications ⋮ Entanglement-assisted quantum codes from matrix-product codes
Uses Software
Cites Work
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- New linear codes from matrix-product codes with polynomial units
- Constructions of new families of nonbinary CSS codes
- Construction and decoding of matrix-product codes from nested codes
- Duality for some families of correction capability optimized evaluation codes
- On the structure of generalized toric codes
- The Magma algebra system. I: The user language
- Decoding affine variety codes using Gröbner bases
- Note on Niederreiter-Xing's propagation rule for linear codes
- List decoding of matrix-product codes from nested codes: an application to quasi-cyclic codes
- A note on orthogonal circulant matrices over finite fields
- Quantum codes from affine variety codes and their subfield-subcodes
- Orthogonal circulant matrices over finite fields, and how to find them
- On the Construction of Nonbinary Quantum BCH Codes
- A Finite Gilbert–Varshamov Bound for Pure Stabilizer Quantum Codes
- Nonbinary Stabilizer Codes Over Finite Fields
- Concatenated Quantum Codes Constructible in Polynomial Time: Efficient Decoding and Error Correction
- On subfield subcodes of modified Reed-Solomon codes (Corresp.)
- Quantum twisted codes
- Error Correcting Codes in Quantum Theory
- Enlargement of Calderbank-Shor-Steane quantum codes
- Nonbinary quantum stabilizer codes
- Quantum error correction via codes over GF(4)
- Quantum Reed-Muller codes
- Lower bound for the quantum capacity of a discrete memoryless quantum channel
- Improved geometric Goppa codes. I. Basic theory
- DECODING OF MATRIX-PRODUCT CODES
- New generalizations of the Reed-Muller codes--I: Primitive codes
- Polynomial weights and code constructions
- On generalized ReedMuller codes and their relatives
- Matrix-product codes over \(\mathbb{F}_q\)
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