Polycyclic codes over Galois rings with applications to repeated-root constacyclic codes
From MaRDI portal
Publication:1931511
DOI10.1016/j.ffa.2012.10.002zbMath1272.94092arXiv1210.0140OpenAlexW2963976753MaRDI QIDQ1931511
Ferruh Özbudak, Hakan Özadam, Steve Szabo, Sergio R. López-Permouth
Publication date: 14 January 2013
Published in: Finite Fields and their Applications (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1210.0140
Gröbner basisGalois ringslinear codesHamming distancecyclic codesconstacyclic codesrepeated-root cyclic codestorsion codes
Algebraic coding theory; cryptography (number-theoretic aspects) (11T71) Linear codes (general theory) (94B05) Cyclic codes (94B15)
Related Items (29)
A transform approach to polycyclic and serial codes over rings ⋮ On a class of repeated-root monomial-like abelian codes ⋮ Lee weights of cyclic self-dual codes over Galois rings of characteristic \(p^2\) ⋮ Multivariable codes in principal ideal polynomial quotient rings with applications to additive modular bivariate codes over \(\mathbb{F}_4\) ⋮ On cyclic codes over Galois rings ⋮ Codes over affine algebras with a finite commutative chain coefficient ring ⋮ Do non-free LCD codes over finite commutative Frobenius rings exist? ⋮ On the structure of repeated-root polycyclic codes over local rings ⋮ On symbol-pair distances of repeated-root constacyclic codes of length \(2p^s\) over \(\mathbb{F}_{p^m}+u\mathbb{F}_{p^m}\) and MDS symbol-pair codes ⋮ Quantum MDS and synchronizable codes from cyclic codes of length \(5p^s\) over \(\mathbb{F}_{p^m}\) ⋮ Optimal constructions of quantum and synchronizable codes from repeated-root cyclic codes of length \(3p^s\) ⋮ On polycyclic codes over a finite chain ring ⋮ A note on: ``Hamming distance of repeated-root constacyclic codes of length \(2p^s\) over \({\mathbb{F}}_{p^m}+u{\mathbb{F}}_{p^m}\) ⋮ A characterization of optimal constacyclic locally repairable codes ⋮ Polycyclic codes over \(\mathbb{F}_{p^m} [u / \langle u^2 \rangle \): classification, Hamming distance, and annihilators] ⋮ Unnamed Item ⋮ Optimal b-symbol constacyclic codes with respect to the Singleton bound ⋮ On the Hamming distances of repeated-root constacyclic codes of length \(4p^s\) ⋮ Additive cyclic codes over finite commutative chain rings ⋮ Polycyclic codes as invariant subspaces ⋮ Hamming distances of constacyclic codes of length \(3p^s\) and optimal codes with respect to the Griesmer and Singleton bounds ⋮ Cyclic Codes over Galois Rings ⋮ On the symbol-pair distances of repeated-root constacyclic codes of length \(2 p^s\) ⋮ The Hamming distances of repeated-root cyclic codes of length \(5 p^s\) ⋮ Hamming distance of repeated-root constacyclic codes of length \(2p^s\) over \({\mathbb{F}}_{p^m}+u{\mathbb{F}}_{p^m} \) ⋮ On the structure of 1-generator quasi-polycyclic codes over finite chain rings ⋮ Quantum MDS and synchronizable codes from cyclic and negacyclic codes of length \(4p^s\) over \(\mathbb{F}_{p^m}\) ⋮ On \(\mathbb{Z}_2\mathbb{Z}_4\)-additive polycyclic codes and their Gray images ⋮ \((f, \sigma, \delta)\)-skew polycyclic codes and their applications to quantum codes
This page was built for publication: Polycyclic codes over Galois rings with applications to repeated-root constacyclic codes
