Relevant bibliographies by topics / Maps over finite fields

Academic literature on the topic 'Maps over finite fields'

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Published: 4 June 2021
Last updated: 5 February 2022

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Journal articles on the topic "Maps over finite fields"

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de Cataldo, Mark Andrea A. "Proper Toric Maps Over Finite Fields." International Mathematics Research Notices 2015, no. 24 (2015): 13106–21. http://dx.doi.org/10.1093/imrn/rnv094.

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Berson, Joost. "Linearized polynomial maps over finite fields." Journal of Algebra 399 (February 2014): 389–406. http://dx.doi.org/10.1016/j.jalgebra.2013.10.013.

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Misiurewicz, Michał, John G. Stevens, and Diana M. Thomas. "Iterations of linear maps over finite fields." Linear Algebra and its Applications 413, no. 1 (February 2006): 218–34. http://dx.doi.org/10.1016/j.laa.2005.09.002.

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Vivaldi, F. "Geometry of linear maps over finite fields." Nonlinearity 5, no. 1 (January 1, 1992): 133–47. http://dx.doi.org/10.1088/0951-7715/5/1/005.

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Küçüksakallı, Ömer. "Value sets of Lattès maps over finite fields." Journal of Number Theory 143 (October 2014): 262–78. http://dx.doi.org/10.1016/j.jnt.2014.04.014.

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DEMPWOLFF, U., J. CHRIS FISHER, and ALLEN HERMAN. "SEMILINEAR TRANSFORMATIONS OVER FINITE FIELDS ARE FROBENIUS MAPS." Glasgow Mathematical Journal 42, no. 2 (May 2000): 289–95. http://dx.doi.org/10.1017/s0017089500020164.

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Mullen, G. L., D. Wan, and Q. Wang. "VALUE SETS OF POLYNOMIAL MAPS OVER FINITE FIELDS." Quarterly Journal of Mathematics 64, no. 4 (October 17, 2012): 1191–96. http://dx.doi.org/10.1093/qmath/has026.

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Morton, Patrick. "Periods of Maps on Irreducible Polynomials over Finite Fields." Finite Fields and Their Applications 3, no. 1 (January 1997): 11–24. http://dx.doi.org/10.1006/ffta.1996.0168.

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Küçüksakallı, Ömer. "Value sets of bivariate Chebyshev maps over finite fields." Finite Fields and Their Applications 36 (November 2015): 189–202. http://dx.doi.org/10.1016/j.ffa.2015.08.005.

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FLYNN, RYAN, and DEREK GARTON. "GRAPH COMPONENTS AND DYNAMICS OVER FINITE FIELDS." International Journal of Number Theory 10, no. 03 (March 18, 2014): 779–92. http://dx.doi.org/10.1142/s1793042113501224.

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For polynomials and rational maps of fixed degree over a finite field, we bound both the average number of components of their functional graphs as well as the average number of periodic points of their associated dynamical systems.
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Dissertations / Theses on the topic "Maps over finite fields"

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Jogia, Danesh Michael Mathematics &amp Statistics Faculty of Science UNSW. "Algebraic aspects of integrability and reversibility in maps." Publisher:University of New South Wales. Mathematics & Statistics, 2008. http://handle.unsw.edu.au/1959.4/40947.

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We study the cause of the signature over finite fields of integrability in two dimensional discrete dynamical systems by using theory from algebraic geometry. In particular the theory of elliptic curves is used to prove the major result of the thesis: that all birational maps that preserve an elliptic curve necessarily act on that elliptic curve as addition under the associated group law. Our result generalises special cases previously given in the literature. We apply this theorem to the specific cases when the ground fields are finite fields of prime order and the function field $mathbb{C}(t)$. In the former case, this yields an explanation of the aforementioned signature over finite fields of integrability. In the latter case we arrive at an analogue of the Arnol'd-Liouville theorem. Other results that are related to this approach to integrability are also proven and their consequences considered in examples. Of particular importance are two separate items: (i) we define a generalization of integrability called mixing and examine its relation to integrability; and (ii) we use the concept of rotation number to study differences and similarities between birational integrable maps that preserve the same foliation. The final chapter is given over to considering the existence of the signature of reversibility in higher (three and four) dimensional maps. A conjecture regarding the distribution of periodic orbits generated by such maps when considered over finite fields is given along with numerical evidence to support the conjecture.
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Voloch, J. F. "Curves over finite fields." Thesis, University of Cambridge, 1985. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.355283.

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Rovi, Carmen. "Algebraic Curves over Finite Fields." Thesis, Linköping University, Department of Mathematics, 2010. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-56761.

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This thesis surveys the issue of finding rational points on algebraic curves over finite fields. Since Goppa's construction of algebraic geometric codes, there has been great interest in finding curves with many rational points. Here we explain the main tools for finding rational points on a curve over a nite eld and provide the necessary background on ring and field theory. Four different articles are analyzed, the first of these articles gives a complete set of table showing the numbers of rational points for curves with genus up to 50. The other articles provide interesting constructions of covering curves: covers by the Hemitian curve, Kummer extensions and Artin-Schreier extensions. With these articles the great difficulty of finding explicit equations for curves with many rational points is overcome. With the method given by Arnaldo García in [6] we have been able to nd examples that can be used to define the lower bounds for the corresponding entries in the tables given in http: //wins.uva.nl/~geer, which to the time of writing this Thesis appear as "no information available". In fact, as the curves found are maximal, these entries no longer need a bound, they can be given by a unique entry, since the exact value of Nq(g) is now known.

At the end of the thesis an outline of the construction of Goppa codes is given and the NXL and XNL codes are presented.

 

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Lockard, Shannon Renee. "Random vectors over finite fields." Connect to this title online, 2007. http://etd.lib.clemson.edu/documents/1181251515/.

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Giuzzi, Luca. "Hermitian varieties over finite fields." Thesis, University of Sussex, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.326913.

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Sharkey, Andrew. "Random polynomials over finite fields." Thesis, University of Glasgow, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.299963.

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Park, Jang-Woo. "Discrete dynamics over finite fields." Connect to this title online, 2009. http://etd.lib.clemson.edu/documents/1252937730/.

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Cooley, Jenny. "Cubic surfaces over finite fields." Thesis, University of Warwick, 2014. http://wrap.warwick.ac.uk/66304/.

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It is well-known that the set of rational points on an elliptic curve forms an abelian group. When the curve is given as a plane cubic in Weierstrass form the group operation is defined via tangent and secant operations. Let S be a smooth cubic surface over a field K. Again one can define tangent and secant operations on S. These do not give S(K) a group structure, but one can still ask for the size of a minimal generating set. In Chapter 2 of the thesis I show that if S is a smooth cubic surface over a field K with at least 4 elements, and if S contains a skew pair of lines defined over K, then any non-Eckardt K-point on either line generates S(K). This strengthens a result of Siksek [20]. In Chapter 3, I show that if S is a smooth cubic surface over a finite field K = Fq with at least 8 elements, and if S contains at least one K-line, then there is some point P > S(K) that generates S(K). In Chapter 4, I consider cubic surfaces S over finite fields K = Fq that contain no K-lines. I find a lower bound for the proportion of points generated when starting with a non-Eckardt point P > S(K) and show that this lower bound tends to 1/6 as q tends to infinity. In Chapter 5, I define c-invariants of cubic surfaces over a finite field K = Fq with respect to a given K-line contained in S, give several results regarding these c-invariants and relate them to the number of points SS(K)S. In Chapter 6, I consider the problem of enumerating cubic surfaces over a finite field, K = Fq, with a given point, P > S(K), up to an explicit equivalence relation.
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Lotter, Ernest Christiaan. "On towers of function fields over finite fields." Thesis, Stellenbosch : University of Stellenbosch, 2007. http://hdl.handle.net/10019.1/1283.

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Thesis (PhD (Mathematical Sciences))--University of Stellenbosch, 2007.
Explicit towers of algebraic function fields over finite fields are studied by considering their ramification behaviour and complete splitting. While the majority of towers in the literature are recursively defined by a single defining equation in variable separated form at each step, we consider towers which may have different defining equations at each step and with arbitrary defining polynomials. The ramification and completely splitting loci are analysed by directed graphs with irreducible polynomials as vertices. Algorithms are exhibited to construct these graphs in the case of n-step and -finite towers. These techniques are applied to find new tamely ramified n-step towers for 1 n 3. Various new tame towers are found, including a family of towers of cubic extensions for which numerical evidence suggests that it is asymptotically optimal over the finite field with p2 elements for each prime p 5. Families of wildly ramified Artin-Schreier towers over small finite fields which are candidates to be asymptotically good are also considered using our method.
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Lötter, Ernest C. "On towers of function fields over finite fields /." Link to the online version, 2007. http://hdl.handle.net/10019.1/1283.

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Books on the topic "Maps over finite fields"

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Moreno, Carlos J. Algebraic curves over finite fields. Cambridge [England]: Cambridge University Press, 1991.

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Projective geometries over finite fields. 2nd ed. Oxford: Clarendon Press, 1998.

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Jacobson, Nathan. Finite-dimensional division algebras over fields. Berlin: Springer, 1996.

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Dmitri, Kaledin, and Tschinkel Yuri, eds. Higher-dimensional geometry over finite fields. Amsterdam, Netherlands: IOS Press, 2008.

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Jacobson, Nathan. Finite-Dimensional Division Algebras over Fields. Berlin, Heidelberg: Springer Berlin Heidelberg, 1996. http://dx.doi.org/10.1007/978-3-642-02429-0.

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Fried, Michael D., ed. Applications of Curves over Finite Fields. Providence, Rhode Island: American Mathematical Society, 1999. http://dx.doi.org/10.1090/conm/245.

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Noriko, Yui, ed. Arithmetic of diagonal hypersurfaces over finite fields. Cambridge: Cambridge University Press, 1995.

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Hansen, Søren Have. Rational points on curves over finite fields. [Aarhus, Denmark: Aarhus Universitet, Matematisk Institut, 1995.

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Alam, Shajahan. Zeta-functions of curves over finite fields. Manchester: UMIST, 1996.

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A, Huang Ming-Deh, ed. Primality testing and Abelian varieties over finite fields. Berlin: Springer-Verlag, 1992.

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Book chapters on the topic "Maps over finite fields"

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Cafure, Antonio, Guillermo Matera, and Ariel Waissbein. "Efficient Inversion of Rational Maps Over Finite Fields." In Algorithms in Algebraic Geometry, 55–77. New York, NY: Springer New York, 2008. http://dx.doi.org/10.1007/978-0-387-75155-9_4.

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Maubach, Stefan, and Roel Willems. "Keller Maps of Low Degree over Finite Fields." In Springer Proceedings in Mathematics & Statistics, 477–93. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-05681-4_26.

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Zippel, Richard. "Factoring over Finite Fields." In Effective Polynomial Computation, 293–302. Boston, MA: Springer US, 1993. http://dx.doi.org/10.1007/978-1-4615-3188-3_18.

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Tsfasman, Michael, Serge Vlǎduţ, and Dmitry Nogin. "Curves over finite fields." In Mathematical Surveys and Monographs, 133–89. Providence, Rhode Island: American Mathematical Society, 2007. http://dx.doi.org/10.1090/surv/139/03.

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Hachenberger, Dirk, and Dieter Jungnickel. "Matrices Over Finite Fields." In Topics in Galois Fields, 297–353. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-60806-4_7.

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Chahal, J. S. "Equations over Finite Fields." In Topics in Number Theory, 147–62. Boston, MA: Springer US, 1988. http://dx.doi.org/10.1007/978-1-4899-0439-3_8.

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Stix, Jakob. "Sections over Finite Fields." In Lecture Notes in Mathematics, 197–205. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-30674-7_15.

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Rosen, Michael. "Polynomials over Finite Fields." In Graduate Texts in Mathematics, 1–9. New York, NY: Springer New York, 2002. http://dx.doi.org/10.1007/978-1-4757-6046-0_1.

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Mignotte, Maurice. "Polynomials Over Finite Fields." In Mathematics for Computer Algebra, 229–88. New York, NY: Springer New York, 1992. http://dx.doi.org/10.1007/978-1-4613-9171-5_6.

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Ireland, Kenneth, and Michael Rosen. "Equations over Finite Fields." In A Classical Introduction to Modern Number Theory, 138–50. New York, NY: Springer New York, 1990. http://dx.doi.org/10.1007/978-1-4757-2103-4_10.

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Conference papers on the topic "Maps over finite fields"

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Wang, Xiuling, Darrell W. Pepper, Yitung Chen, and Hsuan-Tsung Hsieh. "An H-Adaptive Finite Element Model for Constructing 3-D Wind Fields." In ASME 2004 International Mechanical Engineering Congress and Exposition. ASMEDC, 2004. http://dx.doi.org/10.1115/imece2004-60145.

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Calculating wind velocities accurately and efficiently is the key to successfully assessing wind fields over irregular terrain. In the finite element method, decreasing individual element size (increasing the mesh density) and increasing shape function interpolation order are known to improve accuracy. However, computational speed is typically impaired, along with tremendous increases in computational storage. This problem becomes acutely obvious when dealing with atmospheric flows. An h-adaptation scheme, which allows one to start with a coarse mesh that ultimately refines in high gradients regions, can obtain high accuracy at reduced computational time and storage. H-adaptation schemes have been shown to be very effective in compressible flows for capturing shocks [1], but have found limited use in atmospheric wind field simulations [2]. In this paper, an h-adaptive finite element model has been developed that refines and unrefines element regions based upon velocity gradients. An objective analysis technique is applied to generate a mass consistent 3-D flow field utilizing sparse meteorological data. Results obtained from the PSU/NCAR MM5 atmospheric model are used to establish the initial velocity field in lieu of available meteorological tower data. Wind field estimations for the northwest area of Nevada are currently being examined as potential locations for wind turbines.
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Wang, Xiuling, Darrell W. Pepper, Brenda Buck, and Dirk Goossens. "Constructing 3-D Wind Fields for Nellis Dunes in Nevada." In ASME 2008 International Mechanical Engineering Congress and Exposition. ASMEDC, 2008. http://dx.doi.org/10.1115/imece2008-68863.

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An h-adaptive, mass consistent finite element model (FEM) is used to construct 3-D wind fields over irregular terrain utilizing sparse meteorological tower data. The element size in the computational domain is dynamically controlled by a–posteriori error estimator based on the L2 norm. In the h-adaptive FEM algorithm, large element sizes are typically associated with computational regions where the flow is smooth and small errors; small element sizes are attributed to fast changing flow regions and large errors. The adaptive procedure uses mesh refinement/unrefinement to satisfy error criteria. The application of a mass consistent approach essentially poses a least-squares problem in the computational domain. Preliminary results are obtained for constructing 3-D wind fields for Nellis Dunes in Nevada.
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Pepper, Darrell W., and Xiuling Wang. "An Advanced Numerical Model for Assessing 3-D Wind Fields." In ASME 2007 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2007. http://dx.doi.org/10.1115/detc2007-34680.

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An h-adaptive mass consistent finite element model (FEM) is developed for constructing 3-D wind fields over irregular terrain. The h-adaptive FEM allows the element size to be changed dynamically according to local flow and topographic features. The mesh is refined and unrefined to satisfy preset error criteria. Localized high resolution wind fields can be constructed. The FEM model uses a variational method in an integral function that minimizes the variance of the difference between the observed and analyzed variable. Simulation results are presented for constructing 3-D wind fields for two regions in Nevada. The method appears promising for accurately depicting large scale wind fields, especially where high resolution is needed to capture rapidly changing flows associated with local topographic features.
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Wildberger, N. J. "Neuberg cubics over finite fields." In Proceedings of the First SAGA Conference. WORLD SCIENTIFIC, 2008. http://dx.doi.org/10.1142/9789812793430_0027.

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Draper, Stark C., and Sheida Malekpour. "Compressed sensing over finite fields." In 2009 IEEE International Symposium on Information Theory - ISIT. IEEE, 2009. http://dx.doi.org/10.1109/isit.2009.5205666.

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Tan, Vincent Y. F., Laura Balzano, and Stark C. Draper. "Rank minimization over finite fields." In 2011 IEEE International Symposium on Information Theory - ISIT. IEEE, 2011. http://dx.doi.org/10.1109/isit.2011.6033722.

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von zur Gathen, Joachim. "Irreducible trinomials over finite fields." In the 2001 international symposium. New York, New York, USA: ACM Press, 2001. http://dx.doi.org/10.1145/384101.384146.

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Ronyai, Lajos. "Factoring polynomials over finite fields." In 28th Annual Symposium on Foundations of Computer Science. IEEE, 1987. http://dx.doi.org/10.1109/sfcs.1987.25.

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Darbandi, Masoud, Mohammad Reza Ghorbani, and Hamed Darbandi. "The Uncertainties of Continuum-Based CFD Solvers to Perform Microscale Hot-Wire Anemometer Simulations in Flow Fields Close to Transitional Regime." In ASME 2016 5th International Conference on Micro/Nanoscale Heat and Mass Transfer. American Society of Mechanical Engineers, 2016. http://dx.doi.org/10.1115/mnhmt2016-6697.

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In this study, we simulate the flow and heat transfer during hot-wire anemometry and investigate its thermal behavior and physics using the Computational Fluid Dynamics (CFD) tool. In this regard, we use the finite-volume method and solve the compressible Navier-Stokes equations numerically in slightly non-continuum flow fields. We do not use any slip flow model to include the transitional flow physics in our simulations. Using the CFD method, we simulate the flow over hot–wire and evaluate the uncertainty of CFD in thermal simulation of hot-wire in low transitional flow regimes. The domain sizes and the mesh distributions are carefully chosen to avoid boundary condition error appearances. Following the past researches, we do not take into account the conduction heat transfer passing through hot-wire mounting arms in our simulations. Imposing a fixed temperature condition at the face of hot-wire, we simulate the flow over and the heat transfer from hot-wire and calculate the convection heat transfer coefficient and the local Nusselt number values. To be sure of the accuracy of our CFD code, we simulate a number of similar test cases and compare our numerical solutions with the available numerical solutions and/or experimental data.
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Lee, Moon Ho, and Yuri L. Borissov. "On Jacket transforms over finite fields." In 2009 IEEE International Symposium on Information Theory - ISIT. IEEE, 2009. http://dx.doi.org/10.1109/isit.2009.5205783.

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