A5059969175- Coding theory and cryptography
- graph theory and CDMA systems
- Finite Group Theory Research
- Cooperative Communication and Network Coding
- Cellular Automata and Applications
- Quantum Computing Algorithms and Architecture
- Rings, Modules, and Algebras
- Mathematics and Applications
- Advanced Algebra and Geometry
- Error Correcting Code Techniques
- Advanced Wireless Communication Techniques
- Algebraic structures and combinatorial models
- Quantum-Dot Cellular Automata
- History and Theory of Mathematics
- semigroups and automata theory
- Islamic Finance and Communication
- DNA and Biological Computing
- Advanced Topics in Algebra
- Advanced Numerical Analysis Techniques
- Cryptographic Implementations and Security
- Chaos-based Image/Signal Encryption
- Graph Labeling and Dimension Problems
- Advanced biosensing and bioanalysis techniques
- European Linguistics and Anthropology
- History and advancements in chemistry
University of Scranton
2015-2024
Ohio University
2023
University of Chester
2019
Physical Sciences (United States)
2019
Hefei University
2017
Pohang University of Science and Technology
2004
Centre National de la Recherche Scientifique
2002
Université de Limoges
2002
University of Exeter
2002
The alphabet F/sub 2/+uF/sub 2/ is viewed here as a quotient of the Gaussian integers by ideal (2). Self-dual codes with Lee weights multiple 4 are called Type II. They give even unimodular lattices Construction A, while I yield lattices. B makes it possible to realize Leech lattice lattice. There Gray map which maps II into binary fixed point free involution in their automorphism group. Combinatorial constructions use weighing matrices and strongly regular graphs. Gleason-type theorems for...
We study self-dual codes over the ring Z/sub 2k/ of integers modulo 2k with relationships to even unimodular lattices, modular forms, and invariant rings finite groups. introduce Type II which are closely related as a remarkable class generalization binary codes. A construction lattices is given using Several examples given, in particular first extremal code 6/ length 24 constructed, gives new Leech lattice. The complete symmetrized weight enumerators genus g introduced, MacWilliams...
In this correspondence, we investigate binary extremal self-dual codes. Numerous codes and interesting with minimum weight d=14 16 are constructed. particular, the first Type I [86,43,16] code new enumerators which were not previously known to exist for lengths 40,50,52 54 We also determine possible of 66-100.
Linear complementary dual (LCD) codes are binary linear that meet their trivially. We construct LCD using orthogonal matrices, self-dual codes, combinatorial designs and Gray map from over the family of rings Rk. give a programming bound on largest size an code given length minimum distance. make table lower bounds for this function modest values parameters.
Linear complementary dual (LCD) codes are binary linear that meet their trivially. We construct LCD using orthogonal matrices, self-dual codes, combinatorial designs and Gray map from over the family of rings Rk. give a programming bound on largest size an code given length minimum distance. make table lower bounds for this function modest values parameters.
We study Type IV self-dual codes over the commutative rings of order 4. Gleason-type theorems and their shadow are investigated. A mass formula these given. give a classification TV Z/sub 4/ F2+uF/sub 2/ for reasonable lengths. also construct number optimal codes.
We give some characterizations of self-dual codes over rings, specifically 1 11e ring \mathbb{Z}_{2k} , where denotes the \mathbb{Z}/2k\mathbb{Z} integers modulo 2k using (i',hi11cse Remainder Theorem, investigating Type I and II The Chinese Re\prime naindt^{\backslash }t.Theorem plays an important role in study when is I10\{ a prime power, while Hensel lift powerful tool ) ower Ir1 particular, we concentrate on case k=3 use construction A to build unimodular 3-modular lattices.
Secret sharing is an important topic in cryptography and has applications information security. We use self-dual codes to construct secret-sharing schemes. combinatorial properties invariant theory understand the access structure of these describe two techniques determine scheme, first arising from design second Jacobi weight enumerator, theory.
The generalized Gray map is defined for codes over $\mathbb{Z}_{2^k}$. We give bounds the dimension of kernel and rank image a code $\mathbb{Z}_{2^k}$ with given type show that there exists such each in interval kernel. determine when generates linear self-dual families whose generate binary codes. investigate quaternary examine $\mathbb{Z}_4$ code.