The dimension of subcode-subfields of shortened generalized Reed-Solomon codes

DOI10.1007/s10623-012-9628-zzbMath1301.94145arXiv1108.5475OpenAlexW2049979688WikidataQ62582185 ScholiaQ62582185MaRDI QIDQ356722

Michael E. O'Sullivan, Fernando Hernando, Kyle Marshall

Publication date: 26 July 2013

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

Full work available at URL: https://arxiv.org/abs/1108.5475

zbMATH Keywords

minimum distancegeneralized Reed-Solomon codesnew codessubfield-subcodes

Mathematics Subject Classification ID

Algebraic coding theory; cryptography (number-theoretic aspects) (11T71) Finite fields (field-theoretic aspects) (12E20) Coding and information theory (compaction, compression, models of communication, encoding schemes, etc.) (aspects in computer science) (68P30) Applications to coding theory and cryptography of arithmetic geometry (14G50) Cyclic codes (94B15) Arithmetic theory of polynomial rings over finite fields (11T55) Cyclotomy (11T22)

Related Items (6)

On counting subring-submodules of free modules over finite commutative Frobenius rings ⋮ Entanglement-assisted quantum error-correcting codes from subfield subcodes of projective Reed-Solomon codes ⋮ On the dimension of algebraic-geometric trace codes ⋮ New identities relating wild Goppa codes ⋮ An improvement of the Feng-Rao bound for primary codes ⋮ Quantum codes from affine variety codes and their subfield-subcodes

Uses Software

• Magma

Cites Work

• Unnamed Item
• The Magma algebra system. I: The user language
• Proof of conjectures on the true dimension of some binary Goppa codes
• On the dimension of subfield subcodes
• The trace operator and redundancy of Goppa codes
• On subfield subcodes of modified Reed-Solomon codes (Corresp.)
• Fundamentals of Error-Correcting Codes

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