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Let R = F 2 + u F 2 (u 2 = 0) and S = F 2 + u F 2 + u 2 F 2 (u 3 = 0) be two finite commutative chain rings. This paper studies F 2 R S -cyclic codes, which are described as S [ x ] -submodules of the S [ x ] -module F 2 [ x ] ∕ 〈 x r − 1 〉 × R [ x ] ∕ 〈 x s − 1 〉 × S [ x ] ∕ 〈 x t − 1 〉. We study their generator polynomials and the minimal generating sets. We classify each case of the generating sets separately and determine the size of each such case. Free F 2 R S -cyclic codes and separable codes are discussed, and the structural properties of dual codes of free F 2 R S -cyclic codes are investigated. Moreover, we determine the relationship between the generator polynomials of free F 2 R S -cyclic codes and their duals. As applications, we provide several examples of optimal and near-optimal binary codes which are obtained from the Gray images of F 2 R S -cyclic codes. [ABSTRACT FROM AUTHOR]

Despite widespread use of unclean cooking fuels (UCF) in India, evidence from nationally representative data on its association with visual impairment was lacking. We used a population-based nationwide survey of adults aged 45 years and older that included reported UCF and measured visual impairment. We estimated that 44.8% (95% CI: 42.6, 47.1) of older adults in India lived in households that used UCF. Age- and sex-adjusted prevalence of visual impairment was estimated to be 33.0% (95% CI: 31.0, 34.9) in the older population that did not use UCF and 9.0 percentage points (pp) (95% CI: 8.9, 9.1) higher among those who did. Among those who used UCF, age- and sex-adjusted prevalence of low distance vision was 4.3 pp (95% CI: 4.2, 4.4) higher, prevalence of low near vision was 8.0 pp (95% CI: 7.9, 8.1) higher, and prevalence of blindness was 1.0 pp (95% CI: 0.9, 1.0) higher. After controlling for a rich array of sociodemographic characteristics and state fixed effects, we estimated that use of UCF was associated with higher prevalence of visual impairment by 3.2 pp (95% CI: 1.4, 5.0), low distance vision by 1.8 pp (95% CI: 0.7, 2.9), and low near vision by 3.2 pp (95% CI: 1.3, 5.0). Doubly robust estimates of these differences were slightly larger. Blindness was not significantly partially associated with use of UCF (95% CI: -0.4, 0.6). We did not find support for the hypotheses that the visual impairment risk associated with use of UCF was even larger for females and in households without a separate kitchen or ventilation. The older population of India is highly reliant on UCF that is very strongly associated with visual impairment. Impaired vision should not be overlooked among the harms associated with UCF., (Copyright © 2022 The Author(s). Published by Elsevier Ltd.. All rights reserved.)