Linear \(\ell \)-intersection pairs of codes and their applications

DOI10.1007/s10623-019-00676-zzbMath1450.94052arXiv1810.05103OpenAlexW2971236079MaRDI QIDQ2285781

Somphong Jitman, T. Aaron Gulliver, Satanan Thipworawimon, Kenza Guenda

Publication date: 9 January 2020

Published in: Designs, Codes and Cryptography (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1810.05103

zbMATH Keywords

MDS codesgeneralized Reed-Solomon codesentanglement-assisted quantum error correcting codeslinear \(\ell \)-intersection pairslinear complementary pairs

Mathematics Subject Classification ID

Algebraic coding theory; cryptography (number-theoretic aspects) (11T71) Linear codes (general theory) (94B05) Quantum information, communication, networks (quantum-theoretic aspects) (81P45) Quantum coding (general) (81P70) Computational stability and error-correcting codes for quantum computation and communication processing (81P73)

Related Items (22)

New constructions of entanglement-assisted quantum codes ⋮ Asymmetric entanglement-assisted quantum codes: bound and constructions ⋮ \(l\)-LIPs of codes over finite chain rings ⋮ MDS codes with euclidean and Hermitian hulls of flexible dimensions and their applications to EAQECCs ⋮ Linear \(\ell\)-intersection pairs of cyclic and quasi-cyclic codes over a finite field \({\mathbb{F}}_q\) ⋮ Quantum error-correcting codes from the quantum construction \(X\) ⋮ Corrigendum to: ``\(l\)-LIPs of codes over finite chain rings ⋮ Steane enlargement of entanglement-assisted quantum error-correcting codes ⋮ Three classes of new EAQEC MDS codes ⋮ EAQEC codes from two distinct constacyclic codes ⋮ A class of Hermitian dual-containing constacyclic codes and related quantum codes ⋮ On the \(\ell\)-DLIPs of codes over finite commutative rings ⋮ Matrix-product codes related to constacyclic codes and their applications to EAQEC codes ⋮ Galois hulls of special Goppa codes and related codes with application to EAQECCs ⋮ Constructions of new entanglement-assisted quantum MDS and almost MDS codes ⋮ Linear \(\ell\)-intersection pairs of MDS codes and their applications to AEAQECCs ⋮ Linear codes with small hulls in semi-primitive case ⋮ A new construction of linear codes with one-dimensional hull ⋮ Linear codes with arbitrary dimensional hull and their applications to EAQECCs ⋮ QEC and EAQEC codes from cyclic codes over non-chain rings ⋮ Some new families of entanglement-assisted quantum MDS codes derived from negacyclic codes ⋮ Hermitian hulls of constacyclic codes and their applications to quantum codes

Uses Software

• Magma
• Code Tables

Cites Work

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• Linear codes with complementary duals
• The Magma algebra system. I: The user language
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• Entanglement-assisted quantum MDS codes from constacyclic codes with large minimum distance
• Constructions of good entanglement-assisted quantum error correcting codes
• Entanglement-assisted quantum MDS codes constructed from negacyclic codes
• Construction of some codes suitable for both side channel and fault injection attacks
• Entanglement-assisted quantum MDS codes from negacyclic codes
• Euclidean and Hermitian LCD MDS codes
• Galois self-dual constacyclic codes
• Catalytic Quantum Error Correction
• Correcting Quantum Errors with Entanglement
• On MDS codes via Cauchy matrices
• On Linear Complementary Pairs of Codes
• MDS Codes With Hulls of Arbitrary Dimensions and Their Quantum Error Correction

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