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Search Results: 1 - 10 of 21423 matches for " Pramod Kumar Kewat "
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Cyclic codes from the first class two-prime Whiteman's generalized cyclotomic sequence with order 6
Pramod Kumar Kewat,Priti Kumari
Mathematics , 2015,
Abstract: Binary Whiteman's cyclotomic sequences of orders 2 and 4 have a number of good randomness properties. In this paper, we compute the autocorrelation values and linear complexity of the first class two-prime Whiteman's generalized cyclotomic sequence (WGCS-I) of order $d=6$. Our results show that the autocorrelation values of this sequence is four-valued or five-valued if $(n_1-1)(n_2-1)/36$ is even or odd respectively, where $n_1$ and $n_2$ are two distinct odd primes and their linear complexity is quite good. We employ the two-prime WGCS-I of order 6 to construct several classes of cyclic codes over $\mathrm{GF}(q)$ with length $n_1n_2$. We also obtain the lower bounds on the minimum distance of these cyclic codes.
Cyclic codes over the ring $\mathbb{F}_p[u,v,w]/\langle u^2, v^2, w^2, uv-vu, vw-wv, uw-wu \rangle$
Pramod Kumar Kewat,Sarika Kushwaha
Mathematics , 2015,
Abstract: In this paper, we investigate cyclic codes over the ring $ \mathbb{F}_p[u,v,w]\langle u^2,$ $v^2, w^2$, $uv-vu, vw-wv, uw-wu \rangle$, where $p$ is a prime number. Which is a part of family of Frobenius rings. We find a unique set of generators for these codes and characterize the free cyclic codes. We also study the rank and the Hamming distance of these codes. We also constructs some good $p-ary$ codes as the Gray images of these cyclic codes.
Autocorrelation values and Linear complexity of generalized cyclotomic sequence of order four, and construction of cyclic codes
Priti Kumari,Pramod Kumar Kewat
Mathematics , 2015,
Abstract: Let $n_1$ and $n_2$ be two distinct primes with $\mathrm{gcd}(n_1-1,n_2-1)=4$. In this paper, we compute the autocorrelation values of generalized cyclotomic sequence of order $4$. Our results show that this sequence can have very good autocorrelation property. We determine the linear complexity and minimal polynomial of the generalized cyclotomic sequence over $\mathrm{GF}(q)$ where $q=p^m$ and $p$ is an odd prime. Our results show that this sequence possesses large linear complexity. So, the sequence can be used in many domains such as cryptography and coding theory. We employ this sequence of order $4$ to construct several classes of cyclic codes over $\mathrm{GF}(q)$ with length $n_1n_2$. We also obtain the lower bounds on the minimum distance of these cyclic codes.
Cyclic codes from the second class two-prime Whiteman's generalized cyclotomic sequence with order 6
Pramod Kumar Kewat,Priti Kumari
Mathematics , 2015,
Abstract: Let $n_1=ef+1$ and $n_2=ef'+1$ be two distinct odd primes with positive integers $e,\ f,\ f'.$ In this paper, the two-prime Whiteman's generalized cyclotomic sequence of order $e=6$ is employed to construct several classes of cyclic codes over $\mathrm{GF}(q)$ with length $n_1n_2$. The lower bounds on the minimum distance of these cyclic codes are obtained.
Cyclic codes over the ring $\mathbb{F}_p[u,v] / \langle u^k,v^2,uv-vu\rangle$
Bappaditya Ghosh,Pramod Kumar Kewat
Mathematics , 2015,
Abstract: Let $p$ be a prime number. In this paper, we discuss the structures of cyclic codes over the ring $ \mathbb{F}_p[u, v] / \langle u^k, v^2, uv-vu\rangle$. We find a unique set of generators for these codes. We also study the rank and the Hamming distance of these codes.
On the local and global exterior square L-functions
Pramod Kumar Kewat,Ravi Raghunathan
Mathematics , 2012,
Abstract: We show that the local exterior square L-functions of GL_n constructed via the theory of integral representations by Jacquet and Shalika coincide with those constructed by the Langlands-Shahidi method for square integrable representations (and for all irreducible representations when n is even). We also deduce several local and global consequences.
On cyclic codes over the ring $Z_p + uZ_p + ... + u^{k-1}Z_p$
Abhay Kumar Singh,Pramod Kumar Kewat
Mathematics , 2012,
Abstract: In this paper, we study cyclic codes over the ring $ \Z_p + u\Z_p +...+ u^{k-1}\Z_p $, where $u^k =0$. We find a set of generator for these codes. We also study the rank, the dual and the Hamming distance of these codes.
Cyclic codes over the ring $ \Z_p[u, v]/\langle u^2, v^2, uv-vu\rangle$
Pramod Kumar Kewat,Bappaditya Ghosh,Sukhamoy Pattanayak
Mathematics , 2014,
Abstract: Let $p$ be a prime number. In this paper, we study cyclic codes over the ring $ \Z_p[u, v]/\langle u^2, v^2, uv-vu\rangle$. We find a unique set of generators for these codes. We also study the rank and the Hamming distance of these codes. We obtain all except one ternary optimal code of length 12 as the Gray image of the cyclic codes over the ring $ \Z_p[u, v]/\langle u^2, v^2, uv-vu\rangle$. We also characterize the $p$-ary image of these cyclic codes under the Gray map.
Female Infanticide in 19th-Century India: A Genocide?  [PDF]
Pramod Kumar Srivastava
Advances in Historical Studies (AHS) , 2014, DOI: 10.4236/ahs.2014.35022
Abstract: In post-colonial India the female foeticide, a practice evolved from customary female infanticide of pre-colonial and colonial period, committed though in separate incidents, has made it almost a unified wave of mass murder. It does not fulfil the widely accepted existing definition of genocide but the high rate of abortion of legitimate girl-foetus by Indian parents makes their crime a kind of group killing or genocide. The female foeticide in post-colonial India is not a modern phenomenon but was also prevalent in pre-colonial India since antiquity as female infanticide and the custom continued in the 19th century in many communities of colonial India, documentation of which are widely available in various archives. In spite of the Act of 1870 passed by the Colonial Government to suppress the practice, treating it a murder and punishing the perpetrators of the crime with sentence of death or transportation for life, the crime of murdering their girl children did not stop. During a period of five to ten years after the promulgation of the Act around 333 cases of female infanticide were tried and 16 mothers were sentenced to death, 133 to transportation for life and others for various terms of rigorous imprisonment in colonial India excluding British Burma and Assam where no such crime was reported. The present paper, on the basis of unpublished proceedings and files of Judicial and Criminal department of nineteenth century and published documents, presents a critical discussion on consideration of such unified wave of customary criminality as a sexually selective genocide, its concepts and location of female infanticide in selective areas dominated by specific patriarchal ethos of Hinduism alone, the religious and economic causes behind formation of a historically reliant peculiar Indian mind set, its nineteenth century encounter with legislative measures of astounded colonial state still responsible for continuation of such criminality in more sophisticated way with the help of modern technology, and historically reliant patriarchal mind set of post-colonial Indian state.
Purification and Characterization of Glucose-6-Phosphate Dehydrogenase from Pigeon Pea (Cajanus cajan) Seeds  [PDF]
Siddhartha Singh, Pramod Kumar Srivastava
Advances in Enzyme Research (AER) , 2014, DOI: 10.4236/aer.2014.24014
Abstract: Glucose-6-phosphate dehydrogenase has been purified from pigeon pea (Cajanus cajan) seeds and subjected to characterization. The enzyme was purified 123.69 fold with a yield of 21.37% by ammonium sulphate fractionation, PEG-4000 precipitation, CM cellulose column chromatography and DEAE cellulose column chromatography. The catalytically active enzyme is a dimer of 113 KDa with a subunit molecular weight of 55 KDa. Thermal inactivation of enzyme follows first order kinetics at 30°C and 40°C with half life of 6 and 1.5 min respectively. Km value for glucose-6-phosphate and NADP+ was found to be 2.68 mM and 0.75 mM respectively whereas Vmax value was found to be 0.11 U/mL and 0.13 U/mL respectively. The enzyme shows more affinity towards NADP+ than glucose-6-phosphate. The pKa value was found to be 10.41 indicating that the amino acid residue at active site might be lysine. The enzyme exhibited maximum catalytic activity at pH 8.2. The enzyme was found to be highly thermosensitive with gradual loss of activity above 30°C temperature.
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