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Hai Q. Dinh - One of the best experts on this subject based on the ideXlab platform.
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an explicit expression for euclidean self dual cyclic codes over f2m uf2m of length 2s
Discrete Mathematics, 2021Co-Authors: Yuan Cao, Yonglin Cao, Hai Q. Dinh, Guidong Wang, Jirakom SirisrisakulchaiAbstract:Abstract Let F 2 m be the finite field of 2 m elements and s be any positive integer. The existing literature only gives an effective calculation method to represent all distinct Euclidean self-dual cyclic codes of length 2 s over the finite Chain Ring F 2 m + u F 2 m ( u 2 = 0 ) , such as in Cao et al., (2019). As a development of this topic, we provide an explicit expression for each of these self-dual cyclic codes, using binomial coefficients. The Gray image of any self-dual cyclic code over F 2 m + u F 2 m of length 2 s is a self-dual 2 -quasi-cyclic code over F 2 m of length 2 s + 1 . In particular, we give a generator matrix for each of these self-dual 2 -quasi-cyclic codes over F 2 m .
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On the symbol-pair distance of some classes of repeated-root constacyclic codes over Galois Ring
Applicable Algebra in Engineering Communication and Computing, 2021Co-Authors: Hai Q. Dinh, Abhay Kumar Singh, Indivar Gupta, Manoj Kumar Singh, Narendra Kumar, Paravee ManeejukAbstract:Let $$\gamma = 4z-1$$ γ = 4 z - 1 be an unit of Type $$(*^{-})$$ ( ∗ - ) of the Galois Ring $${{\,\mathrm{GR}\,}}(2^a, m)$$ GR ( 2 a , m ) . The $$\gamma$$ γ -constacyclic codes of length $$2^s$$ 2 s over the Galois Ring $${{\,\mathrm{GR}\,}}(2^a, m)$$ GR ( 2 a , m ) are precisely the ideals $$\langle (x +1)^i \rangle$$ ⟨ ( x + 1 ) i ⟩ , $$0 \le i \le 2^sa$$ 0 ≤ i ≤ 2 s a of the Chain Ring $$\mathfrak {R}(a,m, \gamma ) = \dfrac{{{\,\mathrm{GR}\,}}(2^a,m)[x]}{\langle {x^{2^s}} - \gamma \rangle }$$ R ( a , m , γ ) = GR ( 2 a , m ) [ x ] ⟨ x 2 s - γ ⟩ . This structure is used to determine the symbol pair distance of $$\gamma$$ γ -constacyclic codes of length $$2^s$$ 2 s over $${{\,\mathrm{GR}\,}}(2^a, m)$$ GR ( 2 a , m ) . The exact symbol-pair distances for all such $$\gamma$$ γ -constacyclic codes of length $$2^s$$ 2 s over $${{\,\mathrm{GR}\,}}(2^a, m)$$ GR ( 2 a , m ) are obtained. Also, we provide the MDS symbol-pair codes of length $$2^s$$ 2 s over $${{\,\mathrm{GR}\,}}(2^a, m)$$ GR ( 2 a , m ) and some examples are computed.
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hamming distance of repeated root constacyclic codes of length 2p s over mathbb f _ p m u mathbb f _ p m
Applicable Algebra in Engineering Communication and Computing, 2020Co-Authors: Hai Q. Dinh, Abhay Kumar Singh, Atul Gaur, Indivar Gupta, Manoj Kumar Singh, Roengchai TansuchatAbstract:Let p be an odd prime, and $$\delta$$ be an arbitrary unit of the finite Chain Ring $${\mathbb {F}}_{p^m}+u{\mathbb {F}}_{p^m} \,\, (u^2=0)$$. The Hamming distances of all $$\delta$$-constacyclic codes of length $$2p^s$$ over $${\mathbb {F}}_{p^m}+u{\mathbb {F}}_{p^m}$$ are completely determined. We provide some examples from which some codes have better parameters than the existing ones. As applications, we determine all MDS repeated-root $$\delta$$-constacyclic codes of length $$2p^s$$ over $$\mathbb F_{p^m}+u{\mathbb {F}}_{p^m}$$.
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mds symbol pair repeated root constacylic codes of prime power lengths over mathbb f_ p m u mathbb f_ p m
IEEE Access, 2019Co-Authors: Hai Q. Dinh, Abhay Kumar Singh, Poom Kumam, Pardeep Kumar, S Satpati, Woraphon YamakaAbstract:MDS codes have the highest possible error-detecting and error-correcting capability among codes of given length and size. Let p be any prime, and s, m be positive integers. Here, we consider all constacyclic codes of length p s over the Ring R = F p m + uF p m (u 2 = 0). The units of the Ring R are of the form α + uβ and γ, where α, β, γ ∈ F* p m, which provides p m (p m - 1) constacyclic codes. We acquire that the (α + uβ)-constacyclic codes of ps length over R are the ideals 〈(α 0 x - 1) j 〉, 0 ≤ j ≤ 2 p s , of the finite Chain Ring R[x]/〈x ps - (α + uβ)〉 and the γ-constacyclic codes of ps length over R are the ideals of the Ring R[x]/〈x ps - γ〉 which is a local Ring with the maximal ideal 〈u, x - γ 0 〉, but it is not a Chain Ring. In this paper, we obtain all MDS symbol-pair constacyclic codes of length ps over R. We deduce that the MDS symbol-pair constacyclic codes are the trivial ideal (1) and the Type 3 ideal of γ-constacyclic codes for some particular values of p and s. We also present several parameters including the exact symbol-pair distances of MDS constacyclic symbol-pair codes for different values of p and s.
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an explicit representation and enumeration for self dual cyclic codes over f2m uf2m of length 2s
Discrete Mathematics, 2019Co-Authors: Yuan Cao, Yonglin Cao, Hai Q. Dinh, Somphong JitmanAbstract:Abstract Let F 2 m be a finite field of cardinality 2 m and s a positive integer. Using properties for Kronecker product of matrices and calculation for linear equations over F 2 m , an efficient method for the construction of all distinct self-dual cyclic codes with length 2 s over the finite Chain Ring F 2 m + u F 2 m ( u 2 = 0 ) is provided. On that basis, an explicit representation for every self-dual cyclic code of length 2 s over F 2 m + u F 2 m and an exact formula to count the number of all these self-dual cyclic codes are given.
Edris Faizabadi - One of the best experts on this subject based on the ideXlab platform.
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controlling the magnetic susceptibility in an artificial elliptical quantum Ring by magnetic flux and external rashba effect
Journal of Applied Physics, 2015Co-Authors: Mahboubeh Omidi, Edris FaizabadiAbstract:Magnetic susceptibility is investigated in a man-made elliptical quantum Ring in the presence of Rashba spin-orbit interactions and the magnetic flux. It is shown that magnetic susceptibility as a function of magnetic flux changes between negative and positive signs periodically. The periodicity of the Aharonov-Bohm oscillations depends on the geometry of the region where magnetic field is applied, the eccentricity, and number of sites in each Chain Ring (the elliptical Ring is composed of Chain Rings). The magnetic susceptibility sign can be reversed by tuning the Rashba spin-orbit strength as well. Both the magnetic susceptibility strength and sign can be controlled via external spin-orbit interactions, which can be exploited in spintronics and nanoelectronics.
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energy spectrum and persistent current in a nanoscopic elliptical quantum Ring threaded by magnetic flux in the presence of rashba spin orbit interaction
Solid State Communications, 2014Co-Authors: Mahboubeh Omidi, Edris FaizabadiAbstract:Abstract Energy spectrum and persistent current are investigated in an elliptical quantum Ring enclosed by a magnetic flux in the presence of Rashba spin–orbit interaction (RSOI) through a tight-binding model. The elliptical quantum Ring is composed of M Chain Rings with N sites in each Chain Ring. The presence of both elliptical geometry and RSOI leads to the appearance of the energy levels less dependent on magnetic flux in lowest levels in each channel and the splitting of the spin degeneracy. The periodicity of the persistent current oscillations versus magnetic flux is Φ 0 / ( 2 1 − ζ 2 ) (Φ0 is the magnetic flux quantum and ζ is the eccentricity) for an elliptical Ring with odd N in the half-filled energy levels against Φ 0 / 1 − ζ 2 for the case of even N. The behavior of the persistent current versus eccentricity depends on N, M, the energy levels filling, and RSOI strength. Moreover, by raising the RSOI strength, the amplitude of the persistent current oscillates independent of eccentricity. Therefore, an elliptical quantum Ring with the tunable electric field can be applicable as switching devices in nanoelectronics.
Mahboubeh Omidi - One of the best experts on this subject based on the ideXlab platform.
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controlling the magnetic susceptibility in an artificial elliptical quantum Ring by magnetic flux and external rashba effect
Journal of Applied Physics, 2015Co-Authors: Mahboubeh Omidi, Edris FaizabadiAbstract:Magnetic susceptibility is investigated in a man-made elliptical quantum Ring in the presence of Rashba spin-orbit interactions and the magnetic flux. It is shown that magnetic susceptibility as a function of magnetic flux changes between negative and positive signs periodically. The periodicity of the Aharonov-Bohm oscillations depends on the geometry of the region where magnetic field is applied, the eccentricity, and number of sites in each Chain Ring (the elliptical Ring is composed of Chain Rings). The magnetic susceptibility sign can be reversed by tuning the Rashba spin-orbit strength as well. Both the magnetic susceptibility strength and sign can be controlled via external spin-orbit interactions, which can be exploited in spintronics and nanoelectronics.
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energy spectrum and persistent current in a nanoscopic elliptical quantum Ring threaded by magnetic flux in the presence of rashba spin orbit interaction
Solid State Communications, 2014Co-Authors: Mahboubeh Omidi, Edris FaizabadiAbstract:Abstract Energy spectrum and persistent current are investigated in an elliptical quantum Ring enclosed by a magnetic flux in the presence of Rashba spin–orbit interaction (RSOI) through a tight-binding model. The elliptical quantum Ring is composed of M Chain Rings with N sites in each Chain Ring. The presence of both elliptical geometry and RSOI leads to the appearance of the energy levels less dependent on magnetic flux in lowest levels in each channel and the splitting of the spin degeneracy. The periodicity of the persistent current oscillations versus magnetic flux is Φ 0 / ( 2 1 − ζ 2 ) (Φ0 is the magnetic flux quantum and ζ is the eccentricity) for an elliptical Ring with odd N in the half-filled energy levels against Φ 0 / 1 − ζ 2 for the case of even N. The behavior of the persistent current versus eccentricity depends on N, M, the energy levels filling, and RSOI strength. Moreover, by raising the RSOI strength, the amplitude of the persistent current oscillates independent of eccentricity. Therefore, an elliptical quantum Ring with the tunable electric field can be applicable as switching devices in nanoelectronics.
Abhay Kumar Singh - One of the best experts on this subject based on the ideXlab platform.
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On the symbol-pair distance of some classes of repeated-root constacyclic codes over Galois Ring
Applicable Algebra in Engineering Communication and Computing, 2021Co-Authors: Hai Q. Dinh, Abhay Kumar Singh, Indivar Gupta, Manoj Kumar Singh, Narendra Kumar, Paravee ManeejukAbstract:Let $$\gamma = 4z-1$$ γ = 4 z - 1 be an unit of Type $$(*^{-})$$ ( ∗ - ) of the Galois Ring $${{\,\mathrm{GR}\,}}(2^a, m)$$ GR ( 2 a , m ) . The $$\gamma$$ γ -constacyclic codes of length $$2^s$$ 2 s over the Galois Ring $${{\,\mathrm{GR}\,}}(2^a, m)$$ GR ( 2 a , m ) are precisely the ideals $$\langle (x +1)^i \rangle$$ ⟨ ( x + 1 ) i ⟩ , $$0 \le i \le 2^sa$$ 0 ≤ i ≤ 2 s a of the Chain Ring $$\mathfrak {R}(a,m, \gamma ) = \dfrac{{{\,\mathrm{GR}\,}}(2^a,m)[x]}{\langle {x^{2^s}} - \gamma \rangle }$$ R ( a , m , γ ) = GR ( 2 a , m ) [ x ] ⟨ x 2 s - γ ⟩ . This structure is used to determine the symbol pair distance of $$\gamma$$ γ -constacyclic codes of length $$2^s$$ 2 s over $${{\,\mathrm{GR}\,}}(2^a, m)$$ GR ( 2 a , m ) . The exact symbol-pair distances for all such $$\gamma$$ γ -constacyclic codes of length $$2^s$$ 2 s over $${{\,\mathrm{GR}\,}}(2^a, m)$$ GR ( 2 a , m ) are obtained. Also, we provide the MDS symbol-pair codes of length $$2^s$$ 2 s over $${{\,\mathrm{GR}\,}}(2^a, m)$$ GR ( 2 a , m ) and some examples are computed.
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hamming distance of repeated root constacyclic codes of length 2p s over mathbb f _ p m u mathbb f _ p m
Applicable Algebra in Engineering Communication and Computing, 2020Co-Authors: Hai Q. Dinh, Abhay Kumar Singh, Atul Gaur, Indivar Gupta, Manoj Kumar Singh, Roengchai TansuchatAbstract:Let p be an odd prime, and $$\delta$$ be an arbitrary unit of the finite Chain Ring $${\mathbb {F}}_{p^m}+u{\mathbb {F}}_{p^m} \,\, (u^2=0)$$. The Hamming distances of all $$\delta$$-constacyclic codes of length $$2p^s$$ over $${\mathbb {F}}_{p^m}+u{\mathbb {F}}_{p^m}$$ are completely determined. We provide some examples from which some codes have better parameters than the existing ones. As applications, we determine all MDS repeated-root $$\delta$$-constacyclic codes of length $$2p^s$$ over $$\mathbb F_{p^m}+u{\mathbb {F}}_{p^m}$$.
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mds symbol pair repeated root constacylic codes of prime power lengths over mathbb f_ p m u mathbb f_ p m
IEEE Access, 2019Co-Authors: Hai Q. Dinh, Abhay Kumar Singh, Poom Kumam, Pardeep Kumar, S Satpati, Woraphon YamakaAbstract:MDS codes have the highest possible error-detecting and error-correcting capability among codes of given length and size. Let p be any prime, and s, m be positive integers. Here, we consider all constacyclic codes of length p s over the Ring R = F p m + uF p m (u 2 = 0). The units of the Ring R are of the form α + uβ and γ, where α, β, γ ∈ F* p m, which provides p m (p m - 1) constacyclic codes. We acquire that the (α + uβ)-constacyclic codes of ps length over R are the ideals 〈(α 0 x - 1) j 〉, 0 ≤ j ≤ 2 p s , of the finite Chain Ring R[x]/〈x ps - (α + uβ)〉 and the γ-constacyclic codes of ps length over R are the ideals of the Ring R[x]/〈x ps - γ〉 which is a local Ring with the maximal ideal 〈u, x - γ 0 〉, but it is not a Chain Ring. In this paper, we obtain all MDS symbol-pair constacyclic codes of length ps over R. We deduce that the MDS symbol-pair constacyclic codes are the trivial ideal (1) and the Type 3 ideal of γ-constacyclic codes for some particular values of p and s. We also present several parameters including the exact symbol-pair distances of MDS constacyclic symbol-pair codes for different values of p and s.
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on the symbol pair distance of repeated root constacyclic codes of prime power lengths
IEEE Transactions on Information Theory, 2018Co-Authors: Hai Q. Dinh, Abhay Kumar Singh, Bac T Nguyen, Songsak SriboonchittaAbstract:Let $p$ be a prime, and $\lambda$ be a nonzero element of the finite field $\mathbb F_{p^{m}}$ . The $\lambda$ -constacyclic codes of length $p^{s}$ over $\mathbb F_{p^{m}}$ are linearly ordered under set-theoretic inclusion, i.e., they are the ideals $\langle (x-\lambda _{0})^{i} \rangle$ , $0 \leq i \leq p^{s}$ of the Chain Ring $[({\mathbb F_{p^{m}}[x]})/({\langle x^{p^{s}}-\lambda \rangle })]$ . This structure is used to establish the symbol-pair distances of all such $\lambda$ -constacyclic codes. Among others, all maximum distance separable symbol-pair constacyclic codes of length $p^{s}$ are obtained.
Songsak Sriboonchitta - One of the best experts on this subject based on the ideXlab platform.
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on the symbol pair distance of repeated root constacyclic codes of prime power lengths
IEEE Transactions on Information Theory, 2018Co-Authors: Hai Q. Dinh, Abhay Kumar Singh, Bac T Nguyen, Songsak SriboonchittaAbstract:Let $p$ be a prime, and $\lambda$ be a nonzero element of the finite field $\mathbb F_{p^{m}}$ . The $\lambda$ -constacyclic codes of length $p^{s}$ over $\mathbb F_{p^{m}}$ are linearly ordered under set-theoretic inclusion, i.e., they are the ideals $\langle (x-\lambda _{0})^{i} \rangle$ , $0 \leq i \leq p^{s}$ of the Chain Ring $[({\mathbb F_{p^{m}}[x]})/({\langle x^{p^{s}}-\lambda \rangle })]$ . This structure is used to establish the symbol-pair distances of all such $\lambda$ -constacyclic codes. Among others, all maximum distance separable symbol-pair constacyclic codes of length $p^{s}$ are obtained.
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repeated root constacyclic codes of prime power lengths over finite Chain Rings
Finite Fields and Their Applications, 2017Co-Authors: Hai Q. Dinh, Hien D T Nguyen, Songsak SriboonchittaAbstract:Abstract We study the algebraic structure of repeated-root λ -constacyclic codes of prime power length p s over a finite commutative Chain Ring R with maximal ideal 〈 γ 〉 . It is shown that, for any unit λ of the Chain Ring R , there always exists an element r ∈ R such that λ − r p s is not invertible, and furthermore, the ambient Ring R [ x ] 〈 x p s − λ 〉 is a local Ring with maximal ideal 〈 x − r , γ 〉 . When there is a unit λ 0 such that λ = λ 0 p s , the nilpotency index of x − λ 0 in the ambient Ring R [ x ] 〈 x p s − λ 〉 is established. When λ = λ 0 p s + γ w , for some unit w of R , it is shown that the ambient Ring R [ x ] 〈 x p s − λ 〉 is a Chain Ring with maximal ideal 〈 x p s − λ 0 〉 , which in turn provides structure and sizes of all λ -constacyclic codes and their duals. Among other things, situations when a linear code over R is both α - and β -constacyclic, for different units α , β , are discussed.
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repeated root constacyclic codes of prime power length over f p m u u a and their duals
Discrete Mathematics, 2016Co-Authors: Hai Q. Dinh, Sompong Dhompongsa, Songsak SriboonchittaAbstract:The units of the Chain Ring R a = F p m u { u a } = F p m + u F p m + ? + u a - 1 F p m are partitioned into a distinct types. It is shown that for any unit ? of Type k , a unit λ of Type k ? can be constructed, such that the class of λ -constacyclic of length p s of Type k ? codes is one-to-one correspondent to the class of ? -constacyclic codes of the same length of Type k via a Ring isomorphism. The units of R a of the form ? = ? 0 + u ? 1 + ? + u a - 1 ? a - 1 , where ? 0 , ? 1 , ? , ? a - 1 ? F p m , ? 0 ? 0 , ? 1 ? 0 , are considered in detail. The structure, duals, Hamming and homogeneous distances of ? -constacyclic codes of length p s over R a are established. It is shown that self-dual ? -constacyclic codes of length p s over R a exist if and only if a is even, and in such case, it is unique. Among other results, we discuss some conditions when a code is both α - and β -constacyclic over R a for different units α , β .