On the dimension of the subfield subcodes of 1-point Hermitian codes

DOI10.3934/amc.2020054zbMath1466.94051arXiv1906.10444OpenAlexW2999584054MaRDI QIDQ2025360

Sabira El Khalfaoui, Gábor P. Nagy

Publication date: 12 May 2021

Published in: Advances in Mathematics of Communications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1906.10444

zbMATH Keywords

Hermitian codeAG codesubfield subcode

Mathematics Subject Classification ID

Algebraic coding theory; cryptography (number-theoretic aspects) (11T71) Linear codes (general theory) (94B05) Geometric methods (including applications of algebraic geometry) applied to coding theory (94B27) Applications to coding theory and cryptography of arithmetic geometry (14G50)

Uses Software

• McEliece
• GitHub
• HERmitian

Cites Work

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• On the subfield subcodes of Hermitian codes
• Proof of conjectures on the true dimension of some binary Goppa codes
• List Decoding for Binary Goppa Codes
• On the dimension of trace codes
• The true dimension of certain binary Goppa codes
• Attacking and Defending the McEliece Cryptosystem
• Algebraic Function Fields and Codes
• Cryptanalysis of the Niederreiter Public Key Scheme Based on GRS Subcodes
• Compact McEliece Keys from Goppa Codes
• On subfield subcodes of modified Reed-Solomon codes (Corresp.)
• On the equivalence of McEliece's and Niederreiter's public-key cryptosystems
• Goppa codes and trace operator
• Weak keys in the McEliece public-key cryptosystem
• On the decoding of algebraic-geometric codes
• Generalized Berlekamp-Massey decoding of algebraic-geometric codes up to half the Feng-Rao bound
• Quantum Attacks on Public-Key Cryptosystems
• True dimension of some binary quadratic trace Goppa codes

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