Results 31 to 40 of about 529,213 (275)

Graph-Based Classification of Self-Dual Additive Codes over Finite Fields

, 2008
Quantum stabilizer states over GF(m) can be represented as self-dual additive codes over GF(m^2). These codes can be represented as weighted graphs, and orbits of graphs under the generalized local complementation operation correspond to equivalence ...
Danielsen, Lars Eirik
core   +4 more sources

Skew Cyclic Codes Over ℤ₄ + uℤ₄ With Derivation Based on a New Gray Map and Automorphism

IEEE Access
This paper investigates the algebraic structure and properties of skew cyclic codes over the finite chain ring $R = \mathbb {Z}_{4} + u\mathbb {Z}_{4}$ , where $u^{2} = 0$ .
Eda Tekin
doaj   +1 more source

Complementary dual abelian codes in group algebras of some finite abelian groups [PDF]

ITM Web of Conferences
Linear complementary dual codes have become an interesting sub-family of linear codes over finite fields since they can be practically applied in various fields such as cryptography and quantum error-correction. Recently, properties of complementary dual
Jitman Somphong
doaj   +1 more source

An Enumeration of the Equivalence Classes of Self-Dual Matrix Codes

, 2015
As a result of their applications in network coding, space-time coding, and coding for criss-cross errors, matrix codes have garnered significant attention; in various contexts, these codes have also been termed rank-metric codes, space-time codes over ...
Morrison, Katherine
core   +1 more source

Construction of isodual codes from polycirculant matrices

, 2020
Double polycirculant codes are introduced here as a generalization of double circulant codes. When the matrix of the polyshift is a companion matrix of a trinomial, we show that such a code is isodual, hence formally self-dual.
Shi, Minjia, Sole, Patrick, Xu, Li
core   +3 more sources

Triorthogonal codes and self-dual codes

Quantum Information Processing
21 ...
Shi, Minjia, Lu, Haodong, Kim, Jon-Lark, Solé, Patrick   +3 more
openaire   +2 more sources

Quasi-cyclic complementary dual codes

Finite Fields and Their Applications, 2016
LCD codes are linear codes that intersect with their dual trivially. Quasi cyclic codes that are LCD are characterized and studied by using their concatenated structure. Some asymptotic results are derived. Hermitian LCD codes are introduced to that end and their cyclic subclass is characterized.
Güneri, Cem, Özkaya, Buket, Sole, Patrick   +2 more
openaire   +5 more sources

γ-Dual Codes over Finite Commutative Chain Rings

Axioms
In this article, the notion of γ-dual codes over finite chain rings is introduced as an extension of dual codes over finite chain rings. Various characteristics and properties of γ-dual codes over finite chain rings are explored.
Hai Q. Dinh, Hiep L. Thi, Roengchai Tansuchat   +2 more
doaj   +1 more source

Unique Generators for Cyclic Codes of Arbitrary Length over Fpmu/u3 and Their Applications

Journal of Mathematics, 2022
Cyclic codes play a very important role in the history of coding theory since they have good algebraic structures that can be widely used in coding and decoding.
Hongju Li, Ping Yu, Jing Liang, Feng Zhao   +3 more
doaj   +1 more source

The Weight Distributions of Cyclic Codes and Elliptic Curves

, 2011
Cyclic codes with two zeros and their dual codes as a practically and theoretically interesting class of linear codes, have been studied for many years. However, the weight distributions of cyclic codes are difficult to determine.
Qi, Yanfeng, Tang, Chunming, Wang, Baocheng, Xu, Maozhi, Yang, Yixian   +4 more
core   +1 more source