Krishna V. Kaipa
I am an Associate Professor in the Mathematics
at the Indian Institute of Science
Education and Research Pune.
Office: 446 Academic Building. Office Phone: (+9120)25908162
Research Areas: :
- Coding theory, Combinatorics
New results on Deep Holes of Projective Reed-Solomon Codes (in preparation)
Thesis: Topological Charge of Real Finite-Gap sine-Gordon solutions
- Deep Holes of Projective Reed-Solomon Codes (with Jun Zhang and Daqing Wan), IEEE Transactions on Information Theory, (to appear) , arXiv
- An improvement of the asymptotic Elias bound for non-binary codes , IEEE Transactions on Information Theory, vol. 64, Issue 7, 2018
- Deep holes and MDS extensions of Reed-Solomon codes,
IEEE Transactions on Information Theory, Vol. 63, Issue 8, Aug. 2017.
- Counting Generalized Reed-Solomon codes (with P. Beelen, T. Hoholdt and D. Glynn), Advances in the Mathematics of Communication,
Pages: 777 - 790, Volume 11, Issue 4, November 2017 arXiv
- Line polar Grassmann codes of orthogonal type
(with I. Cardinali, L. Giuzzi, and A. Pasini), Jounal of Pure and Applied Algebra, 220 (2016) no.5. 1924-1934.
- An asymptotic formula in q for the number of [n,k] q-ary MDS codes
, IEEE Transactions on Information Theory, 60 (2014), no. 11, 7047–7057.
- Weight spectrum of codes associated with the Grassmannian G(3,7)
(with Harish Pillai), IEEE Transactions on Information Theory, vol.59, no.2, pp.986-993, 2013
- Automorphism groups of Grassmann codes
(with Sudhir Ghorpade), Finite fields and its Applications, vol.23, pp 80-102, 2013
- Multiscale limit for finite-gap Sine-Gordon Solutions and Calculation of Topological Charge using
Theta-functional Formulae (with Peter Grinevich), Proceedings of Steklov Mathematical Institute, September 2009, Volume 266, Issue 1, pp 49-58
- Principal-investigator in SERB project EMR/2016/005578 "Two fundamental problems in Coding Theory" (2017-2020)
- Co-investigator in the Indo-Russia DST-RFBR project INT/RFBR/P-114 "Algebraic Varieties over Finite Fields and Linear Error Correcting Codes"
- Spring 2020: MTH328 Introduction to Error Correcting Codes (Coding theory)
- Fall 2019: MTH318 Combinatorics
- Spring 2019: MTH102 Multivariable Calculus
- Spring 2018: MTH328 Introduction to Error Correcting Codes (Coding theory)
- Fall 2017: MTH417 Ordinary Differential Equations
- Spring 2017: MTH323 Graph Theory
- Fall 2016: MTH318 Combinatorics
- Spring 2016: MTH328 Introduction to Error Correcting Codes (Coding theory)
- Autumn 2015: MTH201 Linear Algebra
- Spring 2015: MTH423 Cryptography
- Fall 2014: MTH422 Algebraic Topology
Courses taught at IISER Bhopal
- Spring 2014: MTH406 Differentiable Manifolds and Lie Groups
- Fall 2013: MTH101 Calculus of one variable
- Spring 2013: MTH406 Differential Geometry of Curves and Surfaces
- Fall 2012: MTH 605 Topology
Courses taught at IIT Bombay
- Spring 2012: MA 106 Linear Algebra
- Fall 2011: MA 521 Theory of Analytic Functions
- Spring 2011: MA 448 Multivariable Calculus
- Fall 2010: MA 417 Ordinary Differential Equations
- Spring 2010: MA 446 Complex Analysis
- Fall 2009: MA 417 Ordinary Differential Equations
- "Deep Holes of Projective Reed-Solomon Codes", IISER Pune, August 2019.
- "On the Existence of Perfect Codes in Hamming Space", IISER Pune, September 2018.
- "The MDS conjecture, completeness of rational normal curves, and the Polynomial method", LAWCI-2018: ICM 2018 satellite conference on Coding and Information theory,
Campinas, Sao Paulo, Brazil, July 2018.
- "Bounds on the size/rate of codes", 14th Annual Discrete Mathematics and Graph Theory conference of DA-IICT, IIT-Gandhinagar and IIIT-Vadodara, June 2018.
- "The questions of Segre in finite geometry", National Conference on Commutative Algebra and Algebraic Geometry (CAAG ) December 2017.
- "Combinatorial Nullstellensatz", IISER Pune, August 2017.
- "On the convexity of the asymptotic information rate for codes". Inter IISER mathematics meeting, May 2017.
- "Deep holes of Reed Solomon Codes", at ECE department IISc-Bangalore, February 2017.
- "Introduction to Error Correcting Codes", Colloquium at IISER-Tirupati, February 2016.
- Six lectures in Multilinear Algebra, NCM sponsored Instructional School for Teachers at SGGS Institute of Technology, Nanded, Maharashtra. December 2015.
- "The MDS Conjecture and the Completeness of Rational
Normal Curves over a finite field" at IISER Pune, September 2015.
- "Grassmannians and Codes" at IISER Pune, June 2014.
- "Number of MDS codes/arcs in Galois geometries: Asymptotics in q" at the International
Conference on "Algebraic geometry and Coding theory" held at IIT-Bombay, December 2013.
- "Symplectic Hodge-Lepage decomposition in positive characteristic" in the Novikov seminar at the Moscow State University, October 2013.
- "Linear Sections of the Grassmannian over finite fields" in the joint Arithmetic seminar
of the Poncelet French-Russian Laboratory of the Independent University of Moscow, and the Institute for Information Transmission problems of the Russian Academy of Sciences, October 2013.
- "Linear sections of Grassmann Varieties over finite fields" in the
Conference "Current Trends in Algebra" held at IISER-Bhopal, August 2013.
- AFS-3 held at Pune University, July 2013 : Lectures on
differential geometry (connections on vector bundles)
- "Weight spectrum of codes associated to the Grassmannian G(3,7)",
Indian Institute of Science Education and Research Bhopal Jun 2012
- "Algebraic-Geometric solutions of sine-Gordon
equation: Topological charge", Tata Institute of Fundamental Research
- CAM, Bangalore, Jun 2012.
- "Linear Codes associated to Grassmann varieties", Indian
Statistical Institute-Bangalore, Jun 2012.
- "Automorphisms of Grassmann and related codes", Chennai Mathematical Institute, Jun 2012.
- ATM school in Geometric Complex Analysis (Delhi Univ. March 2011) : 3 lectures
- Workshop on Differential Geometry at CIMS Benaras Hindu
University May 2011:
- AFS-1 held at IISER Pune, December 2011 : 4 lectures on
diffferential topology (degree theory and applications)