Hermitian self orthogonal code
 Application of Classical Hermitian Self-Orthogonal MDS …)
There is a truncation of a linear code C over {\mathbb F}_{q^2} of length n to a linear over {\mathbb F}_{q^2} of length r \leqslant n which is linearly Hermitian self-orthogonal code if and only if there is an element of P(C) of weight r. Thus, as emphasised in [6], the puncture code is an extremely useful … Zobacz więcej The puncture code P(C) is the intersection of the right-kernel of \mathrm {T}(\mathrm {G}) with {\mathbb F}_q^n. Zobacz więcej The matrix \mathrm {M}(\mathrm {G}) is a parity check matrix for P(C). i.e. \mathrm {M}(\mathrm {G}) is defined over {\mathbb F}_{q} and its right-kernel is P(C). Zobacz więcej For any u,v \in C, for some (a_1,\ldots ,a_k) \in {\mathbb F}_q^k and (b_1,\ldots ,b_k) \in {\mathbb F}_q^k. Since we have that \lambda =(\lambda _1,\ldots ,\lambda _n) is in the right … Zobacz więcej Theorem 4 can allow us to efficiently calculate the puncture code of a linear code. Then for each codeword of weight r in the puncture code, by Theorem 2, we can construct a quantum error correcting code of length r. … Zobacz więcej Witryna1 mar 2024 · The motivation of studying Hermitian self-dual (self-orthogonal) codes over F q 2 was due to their connection to q-ary quantum stabilizer codes [2]. …
Hermitian self orthogonal code
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WitrynaTable 3. Quaternary Hermitian self-orthogonal codes with n ≤ 21, k ≤ 6 and d ≥ 12 21_6_12.4h_prin Witrynalength r6 nwhich is linearly Hermitian self-orthogonal code if and only if there is an element of P(C) of weight r. Thus, as emphasised in [8], the puncture code is an …
Witryna1 paź 2010 · that the code G RS k (b, v 0) is Hermitian self-orthogonal. Now let G RS k ( a , ( β , 1 )) be a Hermitian self-orthogonal [ t + 1 , k ] -generalized RS code … WitrynaTrace and transpose - Hermitian, unitary, normal transformations, real quadratic form. Chapter 6 : Sections 6.8, 6.10 and 6.11 (Omit 6.9) Extended Professional Component (is a part of internal component only, Not to be included in the External Examination question paper)
Witryna1 sty 2024 · This matrix generates a [72, 18, 16] 4 Hermitian self-orthogonal code. We note that while this code is not optimal, some of the codes obtained from its orbit … Witryna28 cze 2024 · Download a PDF of the paper titled New MDS Entanglement-Assisted Quantum Codes from MDS Hermitian Self-Orthogonal Codes, by Hao Chen …
Witryna11 cze 2024 · Hermitian self-orthogonal codes over {\mathbb {F}}_ {q^ {2}} are obtained as the images of constacyclic codes over {\mathbb {F}}_ {q^ {2m}}. Two …
Witryna13 lut 2024 · Quantum maximum-distance-separable (MDS for short) codes are an important class of quantum codes. In this paper, by using Hermitian self-orthogonal … lychee halloween punchWitrynaStabilizer codes can be constructed from self-orthogonal classical linear codes: Theorem 1. [24, 1] Let C be a linear [n,k,d] error-correcting code over the field Fq2 … kingston beach clubWitryna16 sie 2010 · In this paper, we first construct several classes of classical Hermitian self-orthogonal maximum distance separable (MDS) codes. Through these classical … lychee harvestWitrynaTable 3. Classification of Hermitian self-orthogonal codes over F 4.. n\k 3 4 5 6; 6 4 1: 7 4 1: 8 4 4 4 1: 9 6 1 4 2 lychee health factsWitrynaFull Professor, Bankia Award, Multidisciplinary: PhD on Math, 1st Class Honors Eng. with a National Award, Advanced Music Studies by Carnegie Mellon University with interests in scientific computing and collaborative music and video technologies for neurocognitive therapies, functional diversity, education & Arts Director of the Group … kingston beach postcodeWitrynaIn mathematics, a Hermitian matrix (or self-adjoint matrix) is a complex square matrix that is equal to its own conjugate transpose —that is, the element in the i -th row and j … kingston beach early learning centreWitrynaIn this paper, we construct both Euclidean and Hermitian self-orthogonal codes through algebraic geometry codes. More precisely, we show that an arbitrary … lychee heated vest