A5012434439- Coding theory and cryptography
- graph theory and CDMA systems
- Finite Group Theory Research
- Cellular Automata and Applications
- Quantum-Dot Cellular Automata
- Cooperative Communication and Network Coding
- Quantum Computing Algorithms and Architecture
- Rings, Modules, and Algebras
- Cryptographic Implementations and Security
- Algebraic structures and combinatorial models
- DNA and Biological Computing
- Commutative Algebra and Its Applications
- Advanced Topics in Algebra
- Advanced biosensing and bioanalysis techniques
- Quantum Information and Cryptography
- Financial Markets and Investment Strategies
- Error Correcting Code Techniques
- Advanced Algebra and Logic
- Cryptography and Residue Arithmetic
- Advanced Image Processing Techniques
- Cryptography and Data Security
- Numerical methods in engineering
- Computability, Logic, AI Algorithms
- Oxidative Organic Chemistry Reactions
- Educational Methods and Media Use
Ton Duc Thang University
2016-2024
Kent State University
2014-2024
Institute for Computational Science and Technology
2020
Ohio University
2003-2014
North Dakota State University
2004-2005
The structures of cyclic and negacyclic codes length n their duals over a finite chain ring R are established when is not divisible by the characteristic residue field R~. Some cases where R~ also considered. Namely, structure 2/sup t/ /spl Zopf//sub 2//sup m/ that derived.
We study all constacyclic codes of length 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</sup> over GR <i xmlns:xlink="http://www.w3.org/1999/xlink">(Rfr,m</i> ), the Galois extension ring dimension m xmlns:xlink="http://www.w3.org/1999/xlink">Rfr=</i> F <sub xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> +uF . The units ) are forms xmlns:xlink="http://www.w3.org/1999/xlink">alpha</i> , and...
Codes over the ring of integers modulo 4 have been studied by many researchers. Negacyclic codes such that length n code is odd characterized alphabet Zopf <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sub> , and furthermore, generalized to case being a finite commutative chain ring. In this paper, we investigate negacyclic 2 <sup xmlns:xlink="http://www.w3.org/1999/xlink">s</sup> Galois rings. The structure rings GR(2...
Let p be a prime, and λ nonzero element of the finite field F <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</sub> <sup xmlns:xlink="http://www.w3.org/1999/xlink">m</sup> . The λ-constacyclic codes length xmlns:xlink="http://www.w3.org/1999/xlink">s</sup> over are linearly ordered under set-theoretic inclusion, i.e., they ideals 〈(x - xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> ) xmlns:xlink="http://www.w3.org/1999/xlink">i</sup> 〉, 0...
For any odd prime p, a classification of all constacyclic codes length 4p s over 𝔽 p m is obtained, which establishes the algebraic structure in term specified polynomial generators such codes. Among other results, self-dual and LCD cyclic negacylic are obtained. As an example, 36 27 81 listed.
Let $\mathbb{F}_{p^m}$ be a finite field of cardinality $p^m$ and $R = \mathbb{F}_{p^m}[u]/\langle u^2\rangle \mathbb{F}_{p^m}+u\mathbb{F}_{p^m}$ $(u^2 0)$, where $p$ is prime $m$ positive integer. For any $λ∈ \mathbb{F}_{p^m}^{×}$, an explicit representation for all distinct $λ$-constacyclic codes over $R$ length $np^s$ given by canonical form decomposition each code, $s$ $n$ are arbitrary integers satisfying ${\rm gcd}(p,n) 1$. such using its the dual code provided. Moreover,...
The ring R = Fp <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</sup> + uFp has precisely p (p -1) units which are of the forms γ and α uβ, where 0 ≠ α, β, ϵ . Using generator polynomial structures constacyclic codes length xmlns:xlink="http://www.w3.org/1999/xlink">s</sup> over R, Hamming symbol pair distance distributions all such completely determined. As examples, we provide some good with better parameters than known ones.
<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> Various kinds of distances all negacyclic codes length <emphasis><formula formulatype="inline"><tex>$2^{s}$</tex></formula></emphasis> over formulatype="inline"><tex>$\BBZ _{2^{a}}$</tex></formula></emphasis> are completely determined. Using our structure theorems _{2^{a}}$</tex></formula></emphasis>, we first calculate the Hamming such codes, which particularly lead to weight distributions and...
Cyclic codes are an interesting type of linear and have wide applications in communication storage systems due to their efficient encoding decoding algorithms.In coding theory it is often desirable know the weight distribution a cyclic code estimate error correcting capability probability.In this paper, we present recent progress on distributions over finite fields, which had been determined by exponential sums.The with few weights very useful discussed existence conditions...
Let p be an odd prime, q = <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</sup> , R F <sub xmlns:xlink="http://www.w3.org/1999/xlink">q</sub> + uF with u xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> 1, and S vF uvF v uv vu. In this paper, RS-cyclic codes over RS are studied. As application, we present a construction of quantum error-correcting (QECCs) from the RS, which provides new QECCs. We also consider linear complementary dual...