Results 11 to 20 of about 105,712 (106)

On Linear Codes over Finite Singleton Local Rings

Mathematics
The study of linear codes over local rings, particularly non-chain rings, imposes difficulties that differ from those encountered in codes over chain rings, and this stems from the fact that local non-chain rings are not principal ideal rings.
Sami Alabiad, Alhanouf Ali Alhomaidhi, Nawal A. Alsarori   +2 more
doaj   +3 more sources

On Quadratic Inverses for Quadratic Permutation Polynomials over Integer Rings [PDF]

, 2005
An interleaver is a critical component for the channel coding performance of turbo codes. Algebraic constructions are of particular interest because they admit analytical designs and simple, practical hardware implementation.
Ryu, Jonghoon, Takeshita, Oscar Y.
core   +1 more source

On Maximum Contention-Free Interleavers and Permutation Polynomials over Integer Rings [PDF]

, 2005
An interleaver is a critical component for the channel coding performance of turbo codes. Algebraic constructions are of particular interest because they admit analytical designs and simple, practical hardware implementation. Contention-free interleavers
Takeshita, Oscar Y.
core   +2 more sources

The Gilbert-Varshamov Bound for Stabilizer Codes Over $\mathbb{Z}_m$

IEEE Access, 2018
Quantum codes over finite rings have received a great deal of attention in recent years. Compared with quantum codes over finite fields, a notable advantage of quantum codes over finite rings is that they can adapt to quantum physical systems of ...
Nianqi Tang, Zhuo Li, Lijuan Xing, Ming Zhang   +3 more
doaj   +1 more source

Frobenius Local Rings of Length 5 and Index of Nilpotency 3

Mathematics
This paper investigates finite local non-chain rings associated by the well-known invariants p,n,m,l, and k, where p is a prime number. In particular, we provide a comprehensive characterization of Frobenius local rings of length l=5 and index of ...
Sami Alabiad, Alhanouf Ali Alhomaidhi
doaj   +1 more source

Gorenstein Homological Dimension of Groups Through Flat-Cotorsion Modules [PDF]

Mathematics Interdisciplinary Research
‎The representation theory of groups is one of the most interesting examples of the interaction between physics and pure mathematics‎, ‎where group rings play the main role‎.
Ali Hajizamani
doaj   +1 more source

Communication over Finite-Chain-Ring Matrix Channels

, 2014
Though network coding is traditionally performed over finite fields, recent work on nested-lattice-based network coding suggests that, by allowing network coding over certain finite rings, more efficient physical-layer network coding schemes can be ...
Feng, Chen, Kschischang, Frank R., Nóbrega, Roberto W., Silva, Danilo   +3 more
core   +1 more source

Finite Local Rings of Length 4

Axioms
This paper presents a comprehensive characterization of finite local rings of length 4 and with residue field Fpm, where p is a prime number. Such rings have an order of p4m elements.
Sami Alabiad, Alhanouf Ali Alhomaidhi, Nawal A. Alsarori   +2 more
doaj   +1 more source

Codes over Matrix Rings for Space-Time Coded Modulations

, 2010
It is known that, for transmission over quasi-static MIMO fading channels with n transmit antennas, diversity can be obtained by using an inner fully diverse space-time block code while coding gain, derived from the determinant criterion, comes from an ...
Belfiore, Jean-Claude, Oggier, Frederique, Sole, Patrick   +2 more
core   +1 more source

Commutative Chain Rings with Index of Nilpotency 5 and Residue Field ${\mathbb{F}}_{p^m}$

Axioms
This paper gives a thorough characterization of chain rings with index of nilpotency 5 and residue field Fpm, where p represents a prime number, contributing valuable insights to the field of algebraic structures.
Alhanouf Ali Alhomaidhi, Sami Alabiad, Nawal A. Alsarori   +2 more
doaj   +1 more source