scientific article; zbMATH DE number 5232414
From MaRDI portal
Publication:5440688
zbMath1136.20004MaRDI QIDQ5440688
Publication date: 5 February 2008
Title: zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Endomorphism rings; matrix rings (16S50) Group rings (16S34) Group rings of infinite groups and their modules (group-theoretic aspects) (20C07) Group rings of finite groups and their modules (group-theoretic aspects) (20C05) Algebraic systems of matrices (15A30) Units, groups of units (associative rings and algebras) (16U60)
Related Items (56)
\(G\)-codes, self-dual \(G\)-codes and reversible \(G\)-codes over the ring \(\mathscr{B}_{j,k} \) ⋮ Quasi-cyclic codes as cyclic codes over a family of local rings ⋮ Reversible \(G^k\)-codes with applications to DNA codes ⋮ Group rings, \(G\)-codes and constructions of self-dual and formally self-dual codes ⋮ A group induced four-circulant construction for self-dual codes and new extremal binary self-dual codes ⋮ Additive \(G\)-codes over \(\mathbb{F}_q\) and their dualities ⋮ Quaternary group ring codes: ranks, kernels and self-dual codes ⋮ Unnamed Item ⋮ Quadruple bordered constructions of self-dual codes from group rings ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Units of group algebras of non-Abelian groups of order 16 and exponent 4 over \(\mathbb F_{2^k}\). ⋮ On the joins of group rings ⋮ Reversible \(G\)-codes over the ring \(\mathcal{F}_{j, k}\) with applications to DNA codes ⋮ Systems of MDS codes from units and idempotents ⋮ Application of group ring algebra to localized and delocalized quantum states in periodic potentials ⋮ Bordered constructions of self-dual codes from group rings and new extremal binary self-dual codes ⋮ New quantum codes derived from group rings ⋮ New type I binary \([72, 36, 12\) self-dual codes from composite matrices and \(R_1\) lifts] ⋮ Additive skew \(G\)-codes over finite fields ⋮ New self-dual codes from \(2 \times 2\) block circulant matrices, group rings and neighbours of neighbours ⋮ Self-dual codes using bisymmetric matrices and group rings ⋮ $\ast$-Semiclean rings ⋮ New binary quantum codes from group rings and skew group rings ⋮ Group matrix ring codes and constructions of self-dual codes ⋮ Cyclic codes over \({\mathbb{F}}_2 + u{\mathbb{F}}_2 + v{\mathbb{F}}_2 + uv{\mathbb{F}}_2\) ⋮ Double bordered constructions of self-dual codes from group rings over Frobenius rings ⋮ Composite constructions of self-dual codes from group rings and new extremal self-dual binary codes of length 68 ⋮ Unnamed Item ⋮ Unnamed Item ⋮ The reversibility problem for a family of two-dimensional cellular automata ⋮ Cyclic codes over \(R_{k}\) ⋮ Structure of the unitary subgroup of the group algebra 𝔽2n(QD)16 ⋮ New singly and doubly even binary \([72,36,12\) self-dual codes from \(M_2(R)G\)-group matrix rings] ⋮ Constructions for self-dual codes induced from group rings ⋮ Cyclic codes over local Frobenius rings of order 16 ⋮ Cyclic codes over the ring \(F_2+uF_2+vF_2\) ⋮ A class of constacyclic codes from group algebras ⋮ \(2^n\) bordered constructions of self-dual codes from group rings ⋮ Constructing self-dual codes from group rings and reverse circulant matrices ⋮ Representations of group rings and groups ⋮ Composite matrices from group rings, composite \(G\)-codes and constructions of self-dual codes ⋮ A group representation approach to balance of gain graphs ⋮ On *-clean non-commutative group rings ⋮ Composite G-codes over formal power series rings and finite chain rings ⋮ Unit groups of finite group algebras of Abelian groups of order at most 16 ⋮ Extending an established isomorphism between group rings and a subring of the n × n matrices ⋮ An altered four circulant construction for self-dual codes from group rings and new extremal binary self-dual codes. I ⋮ The structure of the unit group of the group algebra $\mathbb{F}_{2^k } A_4 $ ⋮ New self-dual codes of length 68 from a \(2 \times 2\) block matrix construction and group rings ⋮ A modified bordered construction for self-dual codes from group rings ⋮ Unit group of some finite semisimple group algebras ⋮ Maximal entanglement-assisted quantum error correction codes from the skew group ring \(\mathbb{F}_4\rtimes_\varphi G\) by a heuristic search scheme ⋮ New binary self-dual codes of lengths 80, 84 and 96 from composite matrices ⋮ A note on units in \(\mathbb{F}_Q \operatorname{SL} (2, \mathbb{Z}_3)\) ⋮ Skew G-codes
This page was built for publication: