Results 81 to 90 of about 2,635,004 (136)

Constacyclic duadic codes over $${\mathbb {F}}_4$$

Applicable Algebra in Engineering, Communication and Computing, 2021
Duadic codes over finite fields, which were introduced by \textit{J. S. Leon} et al. [IEEE Trans. Inf. Theory 30, 709--714 (1984; Zbl 0575.94013)], are an important class of cyclic codes (See also Chapter 6 in [\textit{W. C. Huffman} and \textit{V. Pless}, Fundamentals of error-correcting codes.
Karbaski, Arezoo Soufi, Samei, Karim, Sepahvand, Tayebeh   +2 more
openaire   +2 more sources

Constacyclic codes and cocycles

Proceedings. 1998 IEEE International Symposium on Information Theory (Cat. No.98CH36252), 2002
Constacyclic codes may naturally be viewed as objects arising from the cohomological concept of a cocycle. Cohomology theory suggests a transformation which is used to show, under certain circumstances, a cyclic code of length mn over a ring R is isomorphic to the direct sum of m constacyclic codes of length n.
openaire   +1 more source

Quantum Constacyclic BCH Codes over Qudits: A Spectral-Domain Approach

arXiv.org
We characterize constacyclic codes in the spectral domain using the finite field Fourier transform (FFFT) and propose a reduced complexity method for the spectral-domain decoder. Further, we also consider repeated-root constacyclic codes and characterize
Shikha Patel, S. Garani
semanticscholar   +1 more source

Quantum convolutional codes derived from constacyclic codes

Modern Physics Letters B, 2014
In this paper, three families of quantum convolutional codes are constructed. The first one and the second one can be regarded as a generalization of Theorems 3, 4, 7 and 8 [J. Chen, J. Li, F. Yang and Y. Huang, Int. J. Theor. Phys., doi:10.1007/s10773-014-2214-6 (2014)], in the sense that we drop the constraint q ≡ 1 ( mod 4).
Tingsu Yan, Xinmei Huang, Yuansheng Tang
openaire   +1 more source

Galois hulls of constacyclic codes over affine algebra rings

arXiv.org
Let $\mathcal A$ the affine algebra given by the ring $\mathbb{F}_q[X_1,X_2,\ldots,X_\ell]/ I$, where $I$ is the ideal $\langle t_1(X_1), t_2(X_2), \ldots, t_\ell(X_\ell) \rangle$ with each $t_i(X_i)$, $1\leq i\leq \ell$, being a square-free polynomial ...
Indibar Debnath, H. Islam, Edgar Mart'inez-Moro, O. Prakash   +3 more
semanticscholar   +1 more source

Optimal constacyclic locally repairable codes

IEEE Communications Letters, 2019
Being part of distributed storage systems, locally repairable codes (LRCs) have drawn great attention in the past years. Inspired by a recent construction of optimal LRCs-based on cyclic codes, constacyclic LRCs are studied in this letter. Specifically, a family of optimal constacyclic $(r,\delta)_{q}$ -LRCs with unbounded length and minimum ...
Zhonghua Sun, Shixin Zhu, Liqi Wang
openaire   +1 more source

New upper bounds on the number of non-zero weights of constacyclic codes

Discrete Mathematics
For any simple-root constacyclic code $\mathcal{C}$ over a finite field $\mathbb{F}_q$, as far as we know, the group $\mathcal{G}$ generated by the multiplier, the constacyclic shift and the scalar multiplications is the largest subgroup of the ...
Li Chen, Yuqing Fu, Hongwei Liu
semanticscholar   +1 more source

The Arithmetic Singleton Bound on the Hamming Distances of Simple-rooted Constacyclic Codes over Finite Fields

arXiv.org
This paper establishes a novel upper bound-termed the arithmetic Singleton bound-on the Hamming distance of any simple-root constacyclic code over a finite field.
Li Zhu, Hongfeng Wu
semanticscholar   +1 more source

Some New Quantum Codes from Constacyclic BCH Codes

International Journal of Theoretical Physics
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Li, Ping, Wei, Yancong, Kai, Xiaoshan, Li, Jin   +3 more
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ϒ – Constacyclic codes over a Frobenius ring and their application to find novel quantum codes

Journal of Discrete Mathematical Sciences & Cryptography
In this work, we use the Hermitian technique to find novel Quantum error correcting codes (𝒬E𝒞𝒞’s) by Constacyclic codes (CCc’s) over the ring ℛ = ℱp2 [𝓊, 𝓋]/(𝓊3 – ω2 𝓊, 𝓋3 – ω2 𝓋), where p is a non-even prime power and ℱ*p 2 = 〈ω〉.
Pooja Soni, M. Pruthi, Arun Kumar Yadav
semanticscholar   +1 more source