Subquadratic time encodable codes beating the Gilbert-Varshamov bound

We construct explicit algebraic geometry codes built from the Garcia-Stichtenoth function field tower beating the Gilbert-Varshamov bound for alphabet sizes at least 192. Messages are identied with functions in certain Riemann-Roch spaces associated with divisors supported on multiple places. Encoding amounts to evaluating these functions at degree one places. By exploiting algebraic structures particular to the Garcia-Stichtenoth tower, we devise an intricate deterministic \omega/2 < 1.19 runtime exponent encoding and 1+\omega/2 < 2.19 expected runtime exponent randomized (unique and list) decoding algorithms. Here \omega < 2.373 is the matrix multiplication exponent. If \omega = 2, as widely believed, the encoding and decoding runtimes are respectively nearly linear and nearly quadratic. Prior to this work, encoding (resp. decoding) time of code families beating the Gilbert-Varshamov bound were quadratic (resp. cubic) or worse

Computing discrete logarithms in subfields of residue class rings

Recent breakthrough methods \cite{gggz,joux,bgjt} on computing discrete logarithms in small characteristic finite fields share an interesting feature in common with the earlier medium prime function field sieve method \cite{jl}. To solve discrete logarithms in a finite extension of a finite field \F, a polynomial h(x) \in \F[x] of a special form is constructed with an irreducible factor g(x) \in \F[x] of the desired degree. The special form of $h(x)$ is then exploited in generating multiplicative relations that hold in the residue class ring \F[x]/h(x)\F[x] hence also in the target residue class field \F[x]/g(x)\F[x]. An interesting question in this context and addressed in this paper is: when and how does a set of relations on the residue class ring determine the discrete logarithms in the finite fields contained in it? We give necessary and sufficient conditions for a set of relations on the residue class ring to determine discrete logarithms in the finite fields contained in it. We also present efficient algorithms to derive discrete logarithms from the relations when the conditions are met. The derived necessary conditions allow us to clearly identify structural obstructions intrinsic to the special polynomial $h(x)$ in each of the aforementioned methods, and propose modifications to the selection of $h(x)$ so as to avoid obstructions.Comment: arXiv admin note: substantial text overlap with arXiv:1312.167

Health, income inequality and climate related disasters at household level: reflections from an Orissa District

Rural households tend to rely heavily on climate-sensitive resources. Climate Change can reduce the availability of these local natural resources, limiting the options for rural households that depend on natural resources for consumption or economic activities. During and after the climate related disasters the health condition of the rural households get adversely affected and hence, reduce the ability to employ themselves in economic activities and income of the households get adversely affected. In this connection, this paper is an attempt to analyze the adverse health effect due to climate related disasters; mostly due to flood. To understand this phenomenon, this work utilizes primary data collected at the household level from select villages of Kendrapada district in Orissa state in India. The sample consists of 150 rural households. We try to link income and health inequality of the sample households and analyze whether climate related disaster and climate shocks have any impact on their health behavior. We have further attempted to check the difference or similarity in health losses based on each coping strategies of the sample households. Using an econometric approach this study further finds the determinants of health impact of the households due to climate related disasters.Climate change, Health, Energy Consumption, Income inequality, Orissa

Energy Consumption Response to Climate Change under Globalization: Options for India

The problem of mitigating climate change has continued to dominate public debates in terms of its origin, sources, potential impacts and possibly adaptation strategies. In this paper, the contributions of energy to the climate change debate are explored. The analysis based on the secondary information shows that the global use of fossil fuels has increased and dominated world energy consumption and supply. This case is quite similar to Indian case and the emissions in Indian are also increasing. To account for the change in CO2 emission, we have followed index decomposition analysis using data from the PROWESS database of the Center for Monitoring Indian Economy. Two factors are considered to account for the changes in emission intensity of Indian economy, namely, (1) output shift among three sectors of the India economy (Agriculture, Service and Manufacturing) and (2) the structural change based on the aggregate output change with respect to the emissions change for the post globalised period. Based on the estimates we found that the structural change in Indian economy from 1991-2007 plays a major role in reducing emission as compared to the output shifts across the sectors. Based on the findings and international experiences, few policy options for Indian case such as; energy pricing reforms, promoting investment in renewable energy technologies and creating public environmental awareness are suggested.Emission; Energy Consumption; Climate Change; Post-Globalization; Policy Instruments

Algebraic Problems Equivalent to Beating Exponent 3/2 for Polynomial Factorization over Finite Fields

The fastest known algorithm for factoring univariate polynomials over finite fields is the Kedlaya-Umans (fast modular composition) implementation of the Kaltofen-Shoup algorithm. It is randomized and takes $\widetilde{O}(n^{3/2}\log q + n \log^2 q)$ time to factor polynomials of degree $n$ over the finite field $\mathbb{F}_q$ with $q$ elements. A significant open problem is if the $3/2$ exponent can be improved. We study a collection of algebraic problems and establish a web of reductions between them. A consequence is that an algorithm for any one of these problems with exponent better than $3/2$ would yield an algorithm for polynomial factorization with exponent better than $3/2$