Galois hulls of linear codes over finite fields

DOI10.1007/s10623-019-00681-2zbMath1452.94116arXiv1809.08053OpenAlexW2974932074WikidataQ127198755 ScholiaQ127198755MaRDI QIDQ2291660

Yanyan Li

Publication date: 31 January 2020

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

Full work available at URL: https://arxiv.org/abs/1809.08053

zbMATH Keywords

monomial equivalencematrix product code\( \ell \)-Galois hull of a linear code\( \ell \)-Galois LCD code

Mathematics Subject Classification ID

Algebraic coding theory; cryptography (number-theoretic aspects) (11T71) Linear codes (general theory) (94B05)

Related Items (15)

On \(\sigma \)-self-orthogonal constacyclic codes over \(\mathbb{F}_{p^m}+u\mathbb{F}_{p^m}\) ⋮ New Galois hulls of generalized Reed-Solomon codes ⋮ Hulls of cyclic serial codes over a finite chain ring ⋮ Two-sided Galois duals of multi-twisted codes ⋮ Construction methods for Galois LCD codes over finite fields ⋮ On MDS codes with Galois hulls of arbitrary dimensions ⋮ Construction of new quantum codes via Hermitian dual-containing matrix-product codes ⋮ Several classes of Galois self-orthogonal MDS codes and related applications ⋮ Galois hulls of constacyclic codes over finite fields ⋮ Several new families of MDS EAQECCs with much larger dimensions and related application to EACQCs ⋮ Linear codes of larger lengths with Galois hulls of arbitrary dimensions and related entanglement-assisted quantum error-correcting codes ⋮ An open problem of \(k\)-Galois hulls and its application ⋮ Galois hulls of special Goppa codes and related codes with application to EAQECCs ⋮ Construction of MDS twisted Reed-Solomon codes and LCD MDS codes ⋮ A NOTE ON k-GALOIS LCD CODES OVER THE RING

Cites Work

• Unnamed Item
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• Complementary dual codes for counter-measures to side-channel attacks
• Matrix-product codes over finite chain rings
• Linear codes with complementary duals
• New entanglement-assisted quantum codes from \(k\)-Galois dual codes
• Galois LCD codes over finite fields
• Constructions of optimal LCD codes over large finite fields
• Euclidean and Hermitian LCD MDS codes
• Linear codes with complementary duals meet the Gilbert-Varshamov bound
• Linearity and complements in projective space
• Galois self-dual constacyclic codes
• Matrix product codes over finite commutative Frobenius rings
• Finding the permutation between equivalent linear codes: the support splitting algorithm
• On $\sigma$ -LCD Codes
• New Constructions of MDS Codes With Complementary Duals
• DECODING OF MATRIX-PRODUCT CODES
• Matrix-product codes over \(\mathbb{F}_q\)

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