1-generator quasi-cyclic and generalized quasi-cyclic codes over the ring \(\frac{\mathbb Z_4[u]}{\langle u^2 - 1\rangle}\)

DOI10.1007/S00200-017-0315-1zbMath1394.94952OpenAlexW2590277140MaRDI QIDQ681327

Yun Gao, Fang-Wei Fu, Jian Gao, Tingting Wu

Publication date: 30 January 2018

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

Full work available at URL: https://doi.org/10.1007/s00200-017-0315-1

zbMATH Keywords

quasi-cyclic codesGray mapgeneralized quasi-cyclic codesnew \(\mathbb {Z}_4\)-linear codes

Mathematics Subject Classification ID

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

Related Items (5)

1-generator two-dimensional quasi-cyclic codes over $\mathbb{Z}_4[u/\langle u^2-1\rangle$] ⋮ Self-dual and LCD double circulant codes over a class of non-local rings ⋮ Unnamed Item ⋮ \(( \sigma, \delta )\)-skew quasi-cyclic codes over the ring \(\mathbb{Z}_4+u\mathbb{Z}_4 \) ⋮ On the structure of 1-generator quasi-polycyclic codes over finite chain rings

Cites Work

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• Structural properties and enumeration of 1-generator generalized quasi-cyclic codes
• Generalized quasi-cyclic codes: Structural properties and code construction
• One generator quasi-cyclic codes over \(\mathbb F_2 + u\mathbb F_2\)
• Cyclic and some constacyclic codes over the ring \(\frac{\mathbb{Z}_4 [u}{\langle u^2 - 1 \rangle}\)]
• The Z/sub 4/-linearity of Kerdock, Preparata, Goethals, and related codes
• On the algebraic structure of quasi-cyclic codes .I. Finite fields
• Quasi-cyclic codes over Z/sub 4/ and some new binary codes

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