Cyclic codes over \(\mathbb{F}_{2^m}[u]/\langle u^k\rangle \) of oddly even length

DOI10.1007/s00200-015-0281-4zbMath1344.94090arXiv1511.05413OpenAlexW2963422053MaRDI QIDQ315737

Yuan Cao, Fang-Wei Fu, Yong-Lin Cao

Publication date: 23 September 2016

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

Full work available at URL: https://arxiv.org/abs/1511.05413

zbMATH Keywords

cyclic codeself-dual codedual codefinite chain ringnon-principal ideal ring

Mathematics Subject Classification ID

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

Related Items

Matrix-product structure of constacyclic codes over finite chain rings \(\mathbb{F}_{p^m}[u/\langle u^e\rangle\)] ⋮ Complete classification of \((\delta + \alpha u^2)\)-constacyclic codes over \(\mathbb{F}_{2^m} [u/\langle u^4 \rangle\) of oddly even length] ⋮ On self-duality and hulls of cyclic codes over \(\frac{\mathbb{F}_{2^m}[u}{\langle u^k\rangle}\) with oddly even length] ⋮ Classification of self-dual cyclic codes over the chain ring \(\mathbb Z_p[u/\langle u^3 \rangle \)] ⋮ An explicit representation and enumeration for negacyclic codes of length \(2^kn\) over \(\mathbb{Z}_4+u\mathbb{Z}_4\) ⋮ On the depth spectrum of repeated-root constacyclic codes over finite chain rings ⋮ The dual code of any \((\delta + \alpha u^2)\)-constacyclic code over \(\mathbb{F}_{2^m} [u \slash \langle u^4 \rangle\) of oddly even length] ⋮ Classification of cyclic codes over a non-Galois chain ring \(\mathbb{Z}_p [u / \langle u^3 \rangle\)]

Cites Work

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• Cyclic codes and self-dual codes over F/sub 2/+uF/sub 2/
• Constacyclic Codes of Length $2^s$ Over Galois Extension Rings of ${\BBF}_{2}+u{\BBF}_2$