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In this paper, we find a necessary and sufficient condition for multi-twisted Reed-Solomon codes to be MDS. In particular, we introduce a new class of MDS double-twisted Reed-Solomon codes C α , t , h , η with twists t = (1 , 2) and hooks h = (0 , 1) over the finite field F q , providing a non-trivial example over F 16 and enumeration over the finite fields of size up to 17. Moreover, we obtain necessary conditions for the existence of multi-twisted Reed-Solomon codes with small dimensional hull. Consequently, we derive conditions for the existence of MDS multi-twisted Reed-Solomon codes with small dimensional hull. [ABSTRACT FROM AUTHOR]

The aphids, Myzus persicae (Sulzer) and Aphis gossypii (Glover) (Hemiptera: Aphididae) and the whiteflies, Trialeurodes vaporariorum (Westwood) and Bemisia tabaci (Gennadius) (Hemiptera: Aleyrodidae) are the most damaging pests of greenhouse crops, which cause vector-borne viral diseases and its damage includes chlorosis, necrosis, and fruit abortion. This review article addresses the protected cultivation of vegetable crops (cucumber, capsicum, tomato, and gerbera), important insect pests of greenhouse crops in India along with its management by entomopathogenic fungi (EPF) and increase in the virulence by different genetically modified techniques. Due to excessive and indiscriminate use of insecticides over the years, these insect pests became resistant to these insecticides. So, there is a need for the effectual substitutes to manage these pests. Biological control is a foundation of integrated pest management (IPM) that plays a key role in the repression of arthropod pests. Among different IPM program, the uses of different microbial formulations are ecofriendly and safe for life and proven a boon for the farmers and entrepreneurs. EPF are the most effective in reducing aphid and whitefly populations on vegetable crops recommending its organic production under greenhouse conditions and could be a part of IPM. In the future, these insect pests will become more resistant to entomopathogens. Some novel techniques such as genetic engineering of fungal formulations will be required to increase the efficiency of various entomopathogens as these techniques are well adopted by countries like the USA, China, and European countries but its use in India and needs to be improved in the near future. [ABSTRACT FROM AUTHOR]

The peach aphid, Myzus persicae (Hemiptera: Aphididae) and silver leaf whitefly, Bemisia tabaci (Hemiptera: Aleyrodidae) are the major pests of capsicum under protected cultivation. The entomopathogenic fungi (EPF) are environmentally safe than the chemical pesticides. In the present study, different EPF formulations, Beauveria bassiana Balsamo (Vuillemin), Lecanicillium lecanii (Zimmerman) Viegas, Metarhizium anisopliae (Metschnikoff) Sorokin, were evaluated along with Azadirachtin 1% for the management of the aphid and the whitefly on capsicum under protected conditions. Result showed that talc formulation of L. lecanii MTCC 956 at 10 and 12 g/l caused 60.5 and 61.6% population reduction for aphid and 60.0 and 61.6% population reduction for whitefly, whereas Azadirachtin 1% at 4 and 5 ml/l caused 71.2 and 74.7% population reduction for aphid and 68.5 and 71.0% population reduction for whitefly after 3rd spray, respectively and were effective in reducing aphid and whitefly populations on capsicum recommending its organic production under protected cultivation and could be a part of integrated pest management program. [ABSTRACT FROM AUTHOR]

In this paper, we propose a novel method for constructing maximum distance separable (MDS) codes based on the extended invertibility and orthogonality of quasigroups. We provide various methods of constructing an orthogonal system of k-ary operations over Q2\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$Q^2$$\end{document} using a special type of k-ary operations over Q, where Q is any arbitrary finite set. Then we use concepts of strong orthogonality of k-ary operations to establish a connection between orthogonality and linear recursive MDS codes. We illustrate these new classes of MDS codes using the proposed techniques and enumerate such codes using SageMath. [ABSTRACT FROM AUTHOR]