Krishna V. Kaipa

Publications:

• 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 arXiv
• Deep holes and MDS extensions of Reed-Solomon codes, IEEE Transactions on Information Theory, Vol. 63, Issue 8, Aug. 2017. arXiv
  
• 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
  

Grants

1. Principal-investigator in SERB project EMR/2016/005578 "Two fundamental problems in Coding Theory" (2017-2020)
2. Co-investigator in the Indo-Russia DST-RFBR project INT/RFBR/P-114 "Algebraic Varieties over Finite Fields and Linear Error Correcting Codes" (2013-2015)



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Teaching

1. Spring 2020: MTH328 Introduction to Error Correcting Codes (Coding theory)
2. Fall 2019: MTH318 Combinatorics
3. Spring 2019: MTH102 Multivariable Calculus
4. Spring 2018: MTH328 Introduction to Error Correcting Codes (Coding theory)
5. Fall 2017: MTH417 Ordinary Differential Equations
6. Spring 2017: MTH323 Graph Theory
7. Fall 2016: MTH318 Combinatorics
8. Spring 2016: MTH328 Introduction to Error Correcting Codes (Coding theory)
9. Autumn 2015: MTH201 Linear Algebra
10. Spring 2015: MTH423 Cryptography
11. Fall 2014: MTH422 Algebraic Topology
    

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    Courses taught at IISER Bhopal
    
12. Spring 2014: MTH406 Differentiable Manifolds and Lie Groups
13. Fall 2013: MTH101 Calculus of one variable
14. Spring 2013: MTH406 Differential Geometry of Curves and Surfaces
15. Fall 2012: MTH 605 Topology
    

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    Courses taught at IIT Bombay
16. Spring 2012: MA 106 Linear Algebra
17. Fall 2011: MA 521 Theory of Analytic Functions
18. Spring 2011: MA 448 Multivariable Calculus
19. Fall 2010: MA 417 Ordinary Differential Equations
20. Spring 2010: MA 446 Complex Analysis
21. Fall 2009: MA 417 Ordinary Differential Equations

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Talks

1. "Deep Holes of Projective Reed-Solomon Codes", IISER Pune, August 2019.
2. "On the Existence of Perfect Codes in Hamming Space", IISER Pune, September 2018.
3. "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.
4. "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.
5. "The questions of Segre in finite geometry", National Conference on Commutative Algebra and Algebraic Geometry (CAAG ) December 2017.
6. "Combinatorial Nullstellensatz", IISER Pune, August 2017.
7. "On the convexity of the asymptotic information rate for codes". Inter IISER mathematics meeting, May 2017.
8. "Deep holes of Reed Solomon Codes", at ECE department IISc-Bangalore, February 2017.
9. "Introduction to Error Correcting Codes", Colloquium at IISER-Tirupati, February 2016.
10. Six lectures in Multilinear Algebra, NCM sponsored Instructional School for Teachers at SGGS Institute of Technology, Nanded, Maharashtra. December 2015.
11. "The MDS Conjecture and the Completeness of Rational Normal Curves over a finite field" at IISER Pune, September 2015.
12. "Grassmannians and Codes" at IISER Pune, June 2014.
13. "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.
14. "Symplectic Hodge-Lepage decomposition in positive characteristic" in the Novikov seminar at the Moscow State University, October 2013.
15. "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.
16. "Linear sections of Grassmann Varieties over finite fields" in the Conference "Current Trends in Algebra" held at IISER-Bhopal, August 2013.
17. AFS-3 held at Pune University, July 2013 : Lectures on differential geometry (connections on vector bundles)
18. "Weight spectrum of codes associated to the Grassmannian G(3,7)", Indian Institute of Science Education and Research Bhopal Jun 2012
19. "Algebraic-Geometric solutions of sine-Gordon equation: Topological charge", Tata Institute of Fundamental Research - CAM, Bangalore, Jun 2012.
    
20. "Linear Codes associated to Grassmann varieties", Indian Statistical Institute-Bangalore, Jun 2012.
21. "Automorphisms of Grassmann and related codes", Chennai Mathematical Institute, Jun 2012.
22. ATM school in Geometric Complex Analysis (Delhi Univ. March 2011) : 3 lectures
23. Workshop on Differential Geometry at CIMS Benaras Hindu University May 2011:
24. AFS-1 held at IISER Pune, December 2011 : 4 lectures on diffferential topology (degree theory and applications)