Some results on quadratic residue codes over the ring Fp + vFp + v2Fp + v3Fp

DOI10.1142/S1793830917500355zbMath1421.94093MaRDI QIDQ5367529

Jian Gao, Fanghui Ma

Publication date: 20 October 2017

Published in: Discrete Mathematics, Algorithms and Applications (Search for Journal in Brave)

zbMATH Keywords

self-dual codesGray mapformally self-dual codesquadratic residue codes

Mathematics Subject Classification ID

Algebraic coding theory; cryptography (number-theoretic aspects) (11T71) Linear codes (general theory) (94B05) Cyclic codes (94B15)

Uses Software

• Magma

Cites Work

• New extremal binary self-dual codes of length 68 from quadratic residue codes over \(\mathbb{F}_2 + u \mathbb{F}_2 + u^2 \mathbb{F}_2\)
• Applications of coding theory to the construction of modular lattices
• The Magma algebra system. I: The user language
• Some results on linear codes over \(\mathbb {F}_p+u\mathbb {F}_p+u^2\mathbb {F}_p\)
• On self-dual cyclic codes over finite chain rings
• Quadratic residue codes over \(\mathbb{F}_p + v \mathbb{F}_p\) and their Gray images
• Quantum codes from cyclic codes over 𝔽q+v𝔽q+v2𝔽q+v3𝔽q
• Quadratic Residue Codes over $$\mathbb {F}_p+v\mathbb {F}_p+v^{2}\mathbb {F}_p$$
• QUADRATIC RESIDUE CODES OVER ℤ₉
• The Z/sub 4/-linearity of Kerdock, Preparata, Goethals, and related codes
• Fundamentals of Error-Correcting Codes

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