Galois invariance, trace codes and subfield subcodes

DOI10.1016/j.ffa.2010.01.002zbMath1191.94130OpenAlexW1981676191MaRDI QIDQ964416

Marta Giorgetti, Andrea Previtali

Publication date: 15 April 2010

Published in: Finite Fields and their Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.ffa.2010.01.002

zbMATH Keywords

trace codessubfield-subcodeGalois invariant

Mathematics Subject Classification ID

Algebraic coding theory; cryptography (number-theoretic aspects) (11T71) Linear codes (general theory) (94B05) Applications to coding theory and cryptography of arithmetic geometry (14G50) Arithmetic codes (94B40)

Related Items (12)

Rank weights for arbitrary finite field extensions ⋮ The Galois variance of constacyclic codes ⋮ Linear cutting blocking sets and minimal codes in the rank metric ⋮ New criteria for MRD and Gabidulin codes and some rank-metric code constructions ⋮ Generalized weights: an anticode approach ⋮ Extension of Overbeck's attack for Gabidulin-based cryptosystems ⋮ The projective general linear group \(\mathrm{PGL}(2, 5^m)\) and linear codes of length \(5^m+1\) ⋮ A Hamada type characterization of the classical geometric designs ⋮ New invariants for incidence structures ⋮ On trace codes and Galois invariance over finite commutative chain rings ⋮ On defining generalized rank weights ⋮ The projective general linear group \(\mathrm{PGL}(2,2^m)\) and linear codes of length \(2^m+1\)

Cites Work

• Unnamed Item
• The theory of cyclic codes and a generalization to additive codes
• On the dimension of subfield subcodes
• On subfield subcodes of modified Reed-Solomon codes (Corresp.)

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