Some new binary quasi-cyclic codes from codes over the ring \(\mathbb F_2 + u\mathbb F_2 + v\mathbb F_2 + uv\mathbb F_2\)

DOI10.1007/s00200-013-0207-yzbMath1347.94074OpenAlexW2190150863MaRDI QIDQ386409

Nuh Aydin, Suat Karadeniz, Bahattin Yildiz

Publication date: 9 December 2013

Published in: Applicable Algebra in Engineering, Communication and Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00200-013-0207-y

zbMATH Keywords

quasi-cyclic codescyclic codesGray mapsLee weight

Mathematics Subject Classification ID

Linear codes (general theory) (94B05) Polynomials, factorization in commutative rings (13P05) Cyclic codes (94B15)

Related Items (8)

Unnamed Item ⋮ New linear codes from constacyclic codes ⋮ Cyclic codes over R3,m ⋮ On codes over Frobenius rings: generating characters, MacWilliams identities and generator matrices ⋮ A note on constacyclic and quasi-cyclic codes over \({\mathbb{F}}_2+u{\mathbb{F}}_2+v{\mathbb{F}}_2+uv{\mathbb{F}}_2\) ⋮ \(( \sigma, \delta )\)-skew quasi-cyclic codes over the ring \(\mathbb{Z}_4+u\mathbb{Z}_4 \) ⋮ The homogeneous weight for Rk, related gray map and new binary quasi-cyclic codes ⋮ $(1-2u^2)$-constacyclic codes over $\mathbb{F}_p+u\mathbb{F}_p+u^2\mathbb{F}_p$

Uses Software

• Magma
• Code Tables

Cites Work

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• Double-circulant and bordered-double-circulant constructions for self-dual codes over \(R_2\)
• Codes over \(R_k\), Gray maps and their binary images
• Linear codes over \({\mathbb{F}_2+u\mathbb{F}_2+v\mathbb{F}_2+uv\mathbb{F}_2}\)
• The Magma algebra system. I: The user language
• Cyclic codes over \({\mathbb{F}}_2 + u{\mathbb{F}}_2 + v{\mathbb{F}}_2 + uv{\mathbb{F}}_2\)
• Variations on Encoding Circuits for Stabilizer Quantum Codes
• New binary one-generator quasi-cyclic codes
• Nine good rate (m-1)/pm quasi-cyclic codes
• Some best rate 1/p and rate (p-1)/p systematic quasi-cyclic codes over GF(3) and GF(4)
• Quasi-cyclic codes over Z/sub 4/ and some new binary codes
• Some new binary, quasi-cyclic codes
• The structure of 1-generator quasi-twisted codes and new linear codes

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