Cyclic codes over R=Fp+uFp+⋯+uk−1Fp with length psn

Han, Mu; Ye, Youpei; Zhu, Shixin; Xu, Chungen; Dou, Bennian

doi:10.1016/j.ins.2010.10.021

Cited by 10 publications

(5 citation statements)

References 13 publications

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“…In this paper, we provide a new way different from the methods used in [7], [9] and [11] to determine the algebraic structures of a class of (δ + αu 2 )constacyclic codes over the finite chain ring F p m [u]/ u e for e = 4.…”

Section: Lemma 12mentioning

confidence: 99%

Evaluation of the impact of Shandong illegal vaccine sales incident on immunizations in China

Zheng

Cao

Cui

et al. 2018

Human Vaccines & Immunotherapeutics

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A case of illegal vaccine sales in Shandong province, China, (hereinafter, the incident), which caused a lack of confidence among vaccination recipients and public panic, was uncovered in March 2016. We conducted a study comprising two cross-sectional surveys: at two months (May 2016) and seven months (October 2016) after the incident. The study aimed to evaluate the impact on immunizations; investigate the variation of the immunization coverage of the National Immunization Program Vaccines (NIPV) and the sales volume growth rate of Category II vaccines; and understand the reasons for non-vaccination and perspectives on immunization. The immunization coverage of NIPV decreased by 5.6 percentage points in the first survey, with a decline of 11.1 in the region of the incident, and decreased by 0.6 in the second survey compared to same period in 2015. The sales volume growth rate of Category II vaccines decreased by 25.8% in the study area and by 48.8% in the region of the incident in April 2016 compared to April 2015. Overall, 15.8% of respondents in the first survey and 7.0% in the second survey did not vaccinate their children according to the NIPV schedule because of the incident (χ = 78.463, P < 0.05). The vaccination was likely affected by the incident in varying degrees, especially in the involved region and particularly in relation to Category II vaccines. Overall, 34% of respondents avoided Category II vaccines for their children, indicating that it will take considerable time to eliminate the negative stigma associated with the incident.

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Section: Lemma 12mentioning

confidence: 99%

Evaluation of the impact of Shandong illegal vaccine sales incident on immunizations in China

Zheng

Cao

Cui

et al. 2018

Human Vaccines & Immunotherapeutics

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show abstract

“…The class of finite chain rings has been extensively used as the alphabet of constacyclic codes [8,[13][14][15][16][17][18][19][20][21][22][23][24]. This class was introduced in [23] to construct new sequences posessing optimal Hamming correlation properties, and these sequences were found to be useful in frequency hopping multiple-access (FHMA) spreading spectrum communication systems.…”

Section: Introductionmentioning

confidence: 99%

“…Ozger et al [22] discussed constacyclic codes over R under the condition p = 2, k = 4. Recently, in [15], Mu Han et al classified cyclic codes of length np s over R in case of r = 1 via DFT. Motivated by the above cited studies, the main objective of this paper is to extend the approach of Han et al [15] and to obtain unique polynomial representations of constacyclic codes of any finite length N over R with arbitrary invariants p, r, and k. This paper is organized as follows.…”

Section: Introductionmentioning

confidence: 99%

Constacyclic Codes over Finite Chain Rings of Characteristic p

Alabiad

Alkhamees

2021

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Let R be a finite commutative chain ring of characteristic p with invariants p,r, and k. In this paper, we study λ-constacyclic codes of an arbitrary length N over R, where λ is a unit of R. We first reduce this to investigate constacyclic codes of length ps (N=n1ps,p∤n1) over a certain finite chain ring CR(uk,rb) of characteristic p, which is an extension of R. Then we use discrete Fourier transform (DFT) to construct an isomorphism γ between R[x]/<xN−λ> and a direct sum ⊕b∈IS(rb) of certain local rings, where I is the complete set of representatives of p-cyclotomic cosets modulo n1. By this isomorphism, all codes over R and their dual codes are obtained from the ideals of S(rb). In addition, we determine explicitly the inverse of γ so that the unique polynomial representations of λ-constacyclic codes may be calculated. Finally, for k=2 the exact number of such codes is provided.

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“…+ u k−1 Z 2 (u k = 0) for the rank and minimal spanning of this family of codes. For the case of m = 1, Han et al [13] studied cyclic codes over R = F p + uF p + . .…”

Section: Introductionmentioning

confidence: 99%

“…In this paper, we study the latter problem for the special case of p = 2, k = 1, n is an odd positive integer and e = 4. Specifically, using linear code theory over finite chain rings we provide a new way different from the methods used in [13], [18] and [20] to give a complete classification and an explicit enumeration for (δ + αu 2 )-constacyclic codes of length 2n over the finite chain ring F 2 m [u]/ u 4 . We will adopt the following notations.…”

Section: Introductionmentioning

confidence: 99%

Complete classification of $(δ+αu^2)$-constacyclic codes over $\mathbb{F}_{2^m}[u]/\langle u^4\rangle$ of oddly even length

Cao,

Cao

2016

Preprint

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Cyclic codes over R=Fp+uFp+⋯+uk−1Fp with length psn

Cited by 10 publications

References 13 publications

Evaluation of the impact of Shandong illegal vaccine sales incident on immunizations in China

Evaluation of the impact of Shandong illegal vaccine sales incident on immunizations in China

Constacyclic Codes over Finite Chain Rings of Characteristic p

Complete classification of $(δ+αu^2)$-constacyclic codes over $\mathbb{F}_{2^m}[u]/\langle u^4\rangle$ of oddly even length

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