On the structure of \(\mathbb{Z}_2 \mathbb{Z}_2 [u^3]\)-linear and cyclic codes

DOI10.1016/j.ffa.2017.03.001zbMath1403.94103OpenAlexW2752902859MaRDI QIDQ2406687

Roger Ten-Valls, Ismail Aydogdu, Siap, Irfan

Publication date: 5 October 2017

Published in: Finite Fields and their Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.ffa.2017.03.001

zbMATH Keywords

dualitylinear codescyclic codes\(\mathbb{Z}_2 \mathbb{Z}_2 [u^3\)-linear cyclic codes]

Mathematics Subject Classification ID

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

Related Items (13)

\(\mathbb{Z}_4\mathbb{Z}_4 [u\)-additive cyclic and constacyclic codes] ⋮ Constacyclic codes of length \((p^r,p^s)\) over mixed alphabets ⋮ \(\mathbb{Z}_2\mathbb{Z}_2[u^4\)-cyclic codes and their duals] ⋮ On \(\mathbb{F}_2 RS\)-cyclic codes and their applications in constructing optimal codes ⋮ On \(\mathbb{Z}_4\mathbb{Z}_4[u^3 \)-additive constacyclic codes] ⋮ Unnamed Item ⋮ On a class of skew constacyclic codes over mixed alphabets and applications in constructing optimal and quantum codes ⋮ ℤ4R-additive cyclic and constacyclic codes and MDSS codes ⋮ Constacyclic codes over mixed alphabets and their applications in constructing new quantum codes ⋮ Self-dual codes over \(\mathbb{F}_2 \times (\mathbb{F}_2+v\mathbb{F}_2)\) ⋮ Galois LCD codes over mixed alphabets ⋮ Quantum codes from cyclic codes over the mixed alphabet structure ⋮ Quantum codes from \(\mathbb{Z}_2\mathbb{Z}_2[u/\langle u^4 \rangle \)-cyclic codes]

Uses Software

• Code Tables

Cites Work

• Unnamed Item
• \(\mathbb Z_2\mathbb Z_4\)-linear codes: Generator matrices and duality
• Cyclic codes over the rings \(\mathbb Z_2 + u\mathbb Z_2\) and \(\mathbb Z_2 + u\mathbb Z_2 + u^2 \mathbb Z_2\)
• ${\mathbb {Z}}_{2}{\mathbb {Z}}_{4}$ -Additive Cyclic Codes, Generator Polynomials, and Dual Codes
• $\BBZ_{2}\BBZ_{4}$ -Additive Cyclic Codes
• On ℤ₂ℤ₂[u-additive codes]
• On ℤ_p^rℤ_p^s-additive codes
• The Z/sub 4/-linearity of Kerdock, Preparata, Goethals, and related codes
• $\mathbb {Z}_{2}\mathbb {Z}_{2}[u$ –Cyclic and Constacyclic Codes]

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