Cover Image

Semisimple group codes and dihedral codes

We consider codes that are given as two-sided ideals in a semisimple finite group algebra \({\mathbb F}_q G\) defined by idempotents constructed from subgroups of \(G\) in a natural way and compute their dimensions and weights. We give a criterion to decide when these ideals are all the minimal two...

Full description

Saved in:

Bibliographic Details
Date:	2018
Main Authors:	Dutra, Flaviana S., Ferraz, Raul A., Milies, C. Polcino
Format:	Article
Language:	English
Published:	Lugansk National Taras Shevchenko University 2018
Subjects:	group code minimal code group algebra idempotent dihedral group quaternion group 94B15 94B60 16S34 20C05
Online Access:	https://admjournal.luguniv.edu.ua/index.php/adm/article/view/785
Tags:	Add Tag No Tags, Be the first to tag this record!
Journal Title:	Algebra and Discrete Mathematics

Institution

Algebra and Discrete Mathematics

Similar Items

Central and non central codes of dihedral 2-groups
by: Gupta, S., et al.
Published: (2022)

Extended binary Golay codes by a group algebra
by: Bortos, Maria Yu., et al.
Published: (2024)

Units of some group algebras of groups of order \(12\) over any finite field of characteristic \(3\)
by: Gildea, Joe, et al.
Published: (2018)

Random walks on finite groups converging after finite number of steps
by: Vyshnevetskiy, A. L., et al.
Published: (2018)

Isodual and self-dual codes from graphs
by: Mallik, S., et al.
Published: (2021)

Construction of self-dual binary \([2^{2k},2^{2k-1},2^k]\)-codes
by: Hannusch, Carolin, et al.
Published: (2016)

On semisimple algebra codes: generator theory
by: Martınez-Moro, Edgar
Published: (2018)

On check character systems over quasigroups and loops
by: Belyavskaya, G. B.
Published: (2018)

Semisimple group codes and dihedral codes
by: Dutra, F.S., et al.
Published: (2009)

On the lattice of cyclic codes over finite chain rings
by: Fotue-Tabue, Alexandre, et al.
Published: (2019)

Connectivity and planarity of power graphs of finite cyclic, dihedral and dicyclic groups
by: Chattopadhyay, Sriparna, et al.
Published: (2018)

On various parameters of \(\mathbb{Z}_q\)-simplex codes for an even integer \(q\)
by: Pandian, P. Chella, et al.
Published: (2015)

A new characterization of alternating groups
by: Asboei, Alireza Khalili, et al.
Published: (2018)

On the group of extensions for the bicrossed product construction for a locally compact group
by: Chapovsky, Yu. A., et al.
Published: (2018)

Groups with small cocentralizers
by: Otal, Javier, et al.
Published: (2018)

On representations of permutations groups as isometry groups of \(n\)-semimetric spaces
by: Gerdiy, Oleg, et al.
Published: (2018)

Trivial units in commutative group rings of \(G\times C_{n}\)
by: Küsmüş, Ömer
Published: (2024)

A survey on pairwise mutually permutable products of finite groups
by: Ballester-Bolinches, A., et al.
Published: (2018)

On Sushchansky \(p\)-groups
by: Bondarenko, Ievgen V., et al.
Published: (2018)

Orbit isomorphic skeleton groups
by: Saha, S.
Published: (2023)

The Thue-Morse substitutions and self-similar groups and algebras
by: Bartholdi, L., et al.
Published: (2023)

A note on two families of \(2\)-designs arose from Suzuki-Tits ovoid
by: Alavi, S. H.
Published: (2023)

Formalization of the mathematical modeling process of adaptive change of code structure in wireless data transmission
by: Horlynskyi, Borys V., et al.
Published: (2019)

Encoding algorithms of information objects in the code of conditional deductions
by: Matov, O. Ya., et al.
Published: (2015)

Group action on bimodule categories
by: Drozd, Yuriy A.
Published: (2018)

The method of parametric adaptation of the check polynomials of the component recursive systematic convulsion code turbo code
by: Kurbet, Pavlo M., et al.
Published: (2024)

A new characterization of finite \(\sigma\)-soluble \(P\sigma T\)-groups
by: Adarchenko, N. M.
Published: (2020)

On Gardam's and Murray's units in group rings
by: Bartholdi, L.
Published: (2023)

Finite intersection of valuation overrings of polynomial rings in at most three variables
by: Paudel, Lokendra
Published: (2024)

Matrix characterization of symmetry groups of boolean functions
by: Jasionowski, Pawel
Published: (2018)

Nonuniqueness of semidirect decompositions for semidirect products with directly decomposable factors and applications for dihedral groups
by: Daugulis, Peteris
Published: (2017)

Serial group rings of finite groups. General linear and close groups
by: Kukharev, Andrei, et al.
Published: (2015)

Graded limits of minimal affinizations and beyond: the multiplicity free case for type \(E_6\)
by: Moura, Adriano, et al.
Published: (2018)

Method of adaptation of cascade codes to ensure reliability of information transmission of wireless data transmission systems
by: Zaitsev, Serhii V., et al.
Published: (2023)

Serial group rings of finite groups. \(p\)-solvability
by: Kukharev, Andrei, et al.
Published: (2018)

Minimal non-\(PC\)-groups
by: Artemovych, Orest D.
Published: (2018)

Finite groups as groups of automata with no cycles with exit
by: Russyev, Andriy
Published: (2018)

Word length in symmetrized presentations of Thompson's group \(F\)
by: Horak, Matthew, et al.
Published: (2018)

On intersections of normal subgroups in groups
by: Kulikova, O. V.
Published: (2018)

On fibers and accessibility of groups acting on trees with inversions
by: Mahmood, Rasheed Mahmood Saleh
Published: (2015)