Hulls of double cyclic codes
Web6 aug. 2024 · The hull plays an important role in determining the complexity of algorithms for checking permutation equivalence of two linear codes and computing the automorphism … Web21 okt. 2014 · The polynomial representation of Z2-double cyclic codes and its duals is given, and the relations between the generator polynomials of these codes are studied. A binary linear code C is a $${\mathbb {Z}} ...
Hulls of double cyclic codes
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Web8 jul. 2024 · In this work, we study the hull of cyclic codes over a finite non chain ring R = Fq+vFq, where v 2 = v. The main tool for the characterization of the hull of cyclic codes … Web21 okt. 2014 · Z2-double cyclic codes. Joaquim Borges, Cristina Fernández-Córdoba, Roger Ten-Valls. A binary linear code is a -double cyclic code if the set of coordinates can be partitioned into two subsets such that any cyclic shift of the coordinates of both subsets leaves invariant the code. These codes can be identified as submodules of the -module …
Web27 feb. 2024 · The hulls of linear and cyclic codes over finite fields have been of interest and extensively studied due to their wide applications. In this paper, the hulls of cyclic codes of length n over the ring Z 4 have been focused on. WebIn this paper, we characterize hulls of double cyclic codes over Z2. Firstly, we give the generators of hulls of double cyclic codes under the separab…
Web29 okt. 2024 · clinical coding Hulls of cyclic codes October 2024 Authors: Alexandre Fotue Tabue University of Bertoua No full-text available ResearchGate has not been able to … In this work, we introduce the $${\mathbb {F}}_qR$$ -linear skew cyclic codes, wh ere $$q=p^s$$ is a prime power and $$R={\mathbb {F}}_q+u{\mathbb {F}}_q$$ with $$u^2=0$$ . We provide the algebraic structure of these codes. The dual codes of separable linear skew cyclic codes are also presented. Meer weergeven Let \vartheta and \varTheta be the automorphisms of {\mathbb {F}}_q and R, respectively. A code C is said to be an {\mathbb {F}}_qR-linear skew cyclic code of length … Meer weergeven [26] Let C be a skew cyclic code of length \beta over R and A be the set of non-zero skew polynomials of minimal degree in C. 1. (1) If there … Meer weergeven The code C is an {\mathbb {F}}_qR-linear skew cyclic code of length \alpha +\beta if and only if C is a left R[x,\varTheta ]-submodule of R_{\alpha ,\beta }. Let {\overleftarrow{f(x)}}^{u} … Meer weergeven Let C be an {\mathbb {F}}_qR-linear skew cyclic code of length \alpha +\beta . 1. (i) If \psi (C)=\langle g_0+ug_1\rangle , then \begin{aligned} C=\langle (f 0),(l_1 g_0+ug_1)\rangle , \end{aligned}where … Meer weergeven
Web5 okt. 2024 · Finally, the hull of each cyclic code with length $2n$ over $\mathbb{F}_{2^m}+u\mathbb{F}_{2^m}$ is determined and all distinct self-orthogonal …
Web1 jan. 2024 · In this paper, we focus on the study of the hulls of cyclic codes of length n over a finite chain ring R of parameters (p, r, a, e, r) such that n and p are coprime. This is the … ny speech hearingWebHulls of Cyclic Codes over the Ring F2 + vF2 Jitman Thai Journal of Mathematics Home > Special Issue (2024): IMT-GT International Conference on Mathematics, Statistics and Their Applications 2024 > Jitman magicshine monteer 3500 ukWebFirstly, we give the generators of hulls of double cyclic codes under the separable case and the non-separable case with coprime odd block lengths. Then, using the concept of a … ny speed cameras flashesWeb5 dec. 2024 · We provided an explicit representation for each cyclic code, gave clear formulas to calculate the number of codewords in each code and the number of all these … magicshine monteerWebHulls of Cyclic Codes over the Ring F2 + vF2 Hulls of linear codes over finite fields have been introduced and become of interest due to their wide practical applications. … magicshine monteer 8000s ukWeb31 jan. 2024 · The hulls of linear and cyclic codes have been extensively studied due to their wide applications. The dimensions and average dimension of the Euclidean hull of … magicshine monteer 6500 lightWeb1 mei 2015 · In Table 2, we provide the dimensions of the hulls of cyclic codes over F 2 of lengths 1 to 40 together with the corresponding number of cyclic codes of each hull dimension. In Table 2, “n” is the length of the cyclic codes, “dim” refers to the dimension of the hulls of such codes, and “No.” is the number of cyclic codes of length n over F 2 … ny speed ticket