Hermitian dual
Witryna5 paź 2024 · A Hermitian matrix can be diagonalized if and only if it has no right subeigenvalues. Then we present the singular value decomposition for general dual … Witrynadefinite hermitian form h; an OK-submodule Lof V is called an OK-lattice if it is finitely generated and contains a K-basis of V. Since his positive definite, the “norm” function x7→h(x,x) admits a minimum on such a lattice L, denoted by Nh(L), which is attained on a finite set Sh(L). One defines the hermitian dual of Las (1) L# = {y ...
Hermitian dual
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Witrynaquasi-cycliccodes to intersect their dual trivially underEuclidean,Hermitian,and symplecticinner products. Finally, we present a practical method for constructing LCD codes using quasi-cyclic codes and give some examples of good quasi-cyclicEuclidean, Hermitian, and symplectic LCD codes. The paper is organized as follows. WitrynaThe dimension of such Hermitian dual-containing negacyclic codes is completely determined by analyzing cyclotomic cosets. Quantum negacyclic BCH codes of length n = q 2 m − 1 2 are obtained by using Hermitian construction. The constructed quantum negacyclic BCH codes produce new quantum codes with parameters better than …
WitrynaThe term Hermitian form may also refer to a different concept than that explained below: it may refer to a certain differential form on a Hermitian manifold. A complex Hermitian form (also called a symmetric sesquilinear form ), is a sesquilinear form h : V × V → C {\displaystyle h:V\times V\to \mathbb {C} } such that Witrynalength n is called Hermitian self-dual if C = C⊥H, where C⊥H denotes the Hermitian dual code of C which is defined as C⊥H:= {v ∈Fn q u·v = 0 for all u ∈C}. Most of the results in this paper are stated for Fq-linear codes with usual inner product but it can be re-phrased with equal validity to the case of the codes with the ...
Witryna27 lip 2024 · In this paper, we study a family of constacyclic BCH codes over 𝔽_q^2 of length n=q^2m-1/q+1, where q is a prime power, and m≥2 an even integer. The … Witrynadual numbers. 1. Introduction. In this paper, we consider two possible generalizations of Singular Value Decomposition ( T-SVD and ∗ -SVD) to matrices over the ring of dual numbers. We prove that both generalizations always exist. Both types of SVD are motivated by applications. A dual number is a number of the form a + b ϵ where a, b …
Witryna26 maj 2024 · A new criterion for the existence of Hermitian dual-containing cyclic codes is obtained based on a characterization of q-cyclotomic cosets modulo n, and enables us to construct several classes of quantum maximum-distance-separable (MDS) codes from classical Hermitians dual- containing cyclic code. ABSTRACT A new criterion for the …
WitrynauBLAS is a C++ template class library that provides BLAS level 1, 2, 3 functionality for dense, packed and sparse matrices. Eigen is a C++ template library for linear algebra: matrices, vectors, numerical solvers, and related algorithms. Fastor is a high performance tensor (fixed multi-dimensional array) library for modern C++. pyhimykset keskiajallaWitrynaHermitian complementary dual) are determined together with the number of such codes. A new family of MDS constacyclic Hermitian self-dual codes overFq2 is introduced in Section 5. The decomposition for quasi-cyclic codes is generalized to thecase of quasi-twisted codes in Section 6. The number of (λ,ℓ)-QT Hermitian self-dual codes of ... barbara mccarthy judge duiWitryna14 mar 2024 · The Hermitian dual codes of several classes of BCH codes. Abstract: As a special subclass of cyclic codes, BCH codes are usually among the best cyclic codes and have wide applications in communication and storage systems and consumer electronics. Let C be a q 2 -ary BCH code of length n with respect to an n -th primitive … barbara mayer-trautmannWitryna27 lip 2024 · The parameters of quantum codes are derived as a function of their design parameters of the associated constacyclic BCH codes over $\\mathbb{F}_{q^2}$ of length n, showing that with the same lengths, except for three trivial cases, the resultant quantum codes can always yield strict dimension or minimum distance gains. In this … barbara mccabe obituaryWitryna5 paź 2024 · A Hermitian matrix can be diagonalized if and only if it has no right subeigenvalues. Then we present the singular value decomposition for general dual complex matrices. The results are further extended to dual quaternion matrices. Subjects: Rings and Algebras (math.RA) Cite as: arXiv:2110.02050 [math.RA] barbara mcalister artWitrynacan be transformed to non-Hermitian orthogonality on a contour due to a special identity [3, Lemma 3.1], and rigorous analysis is possible. The same identity was used in [22] in a study on moments of complex Ginibre matrices. Multiple orthogonality plays a role in [6,16,18], where it can be treated by using large size pyhimys jättiläinen sanatWitrynaConsidering M being a complex n − dimensional manifold, the tangent bundle T M to M can be seen as a holomorphic vector bundle. In fact, if we consider T M C := T M ⊗ R C then it splits as. T M C = T M ′ ⊕ T M ″, where the spaces on the decomposition are the eigenspaces associated to the extension to T M C of the standard complex ... pyhiinvaellus suomi