Krishna V. Kaipa

I am an Associate Professor in the Mathematics department at the Indian Institute of Science Education and Research Pune.
Office: 446 Academic Building. Office Phone: (+9120)25908162

Research Areas: :

Coding theory, Combinatorics

Preprints:

The error distance distribution of Projective Reed-Solomon Codes (in preparation with Nupur Patanker, and Puspendu Pradhan)

Incidence of lines, points, and planes in PG(3,q) with respect to the twisted cubic (with Puspendu Pradhan), arXiv

On the PGL_2(q)-orbits of lines of PG(3,q) and binary quartic forms (with Nupur Patanker, and Puspendu Pradhan), arXiv

Publications:

On the PGL_2(q)-orbits of lines of PG(3,q) and binary quartic forms in characteristic three (with Puspendu Pradhan), Finite Fields and Their Applications, Volume 111, 2026, arXiv
Higher weight spectra of ternary codes associated to the quadratic Veronese 3-fold (with Puspendu Pradhan) Journal of Algebra and Its Applications. Volume 24, Issue 13n14, 2541007 (2025), arXiv
On the cardinality of matrices with prescribed rank and partial trace over a finite field (with Kumar Balasubramanian and Himanshi Khurana) Linear Algebra Appl. 704 (2025), 35--57, arXiv
Deep Holes of Projective Reed-Solomon Codes (with Jun Zhang and Daqing Wan), IEEE Transactions on Information Theory 66 (2020), no. 4, 2392 -- 2401 , 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

Thesis: Topological Charge of Real Finite-Gap sine-Gordon solutions

Grants

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" (2013-2015)

Teaching

January 2026: MT3254 Introduction to Error Correcting Codes (Coding theory)
August 2025: MT3334 Advanced Linear Algebra
January 2025: MT1213 Calculus II
January 2024: MT2233 Discrete Structures
January 2024: MT3254 Introduction to Error Correcting Codes (Coding theory)
January 2023: MT3254 Introduction to Error Correcting Codes (Coding theory)
August 2022: MT1113 Calculus I
January 2022: MT3254 Introduction to Error Correcting Codes (Coding theory)
August 2021: MT3154 Graph Theory
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

Talks
1. "Some problems in Finite geometry associated to Rational normal curves", GANIT Seminar Series, IIT-Gandhinagar, November 2025.
2. "PGL_2(q)-orbits of lines of P^3(F_q) and binary quartic forms in characteristic 3", IISER Pune, August 2025.
3. "Distribution of number of rational points of intersection of quadrics in projective 3-space over a finite field", IISER Pune, January 2025.
4. "Generalized weight enumerator of Projective Reed Muller codes of order 2", IIT Bombay - Virginia Tech Joint Workshop on Algebraic Coding Theory, IIT-Bombay, August 2024.
5. "Binary quartic forms up to PGL_2 equivalence over a finite field", Workshop on Group theory, IISER Pune, February 2024.
6. "On the classification of lines of PG(3,q) with respect to the twisted cubic", NISER Bhubaneshwar, October 2023.
7. "Two problems in finite geometry", IISER Pune, November 2023.
8. "Waring rank of binary forms over finite fields", IISER Pune, March 2023.
9. "Deep Holes of Projective Reed-Solomon Codes", IISER Pune, August 2019.
10. "On the Existence of Perfect Codes in Hamming Space", IISER Pune, September 2018.
11. "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.
12. "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.
13. "The questions of Segre in finite geometry", National Conference on Commutative Algebra and Algebraic Geometry (CAAG ) December 2017.
14. "Combinatorial Nullstellensatz", IISER Pune, August 2017.
15. "On the convexity of the asymptotic information rate for codes". Inter IISER mathematics meeting, May 2017.
16. "Deep holes of Reed Solomon Codes", at ECE department IISc-Bangalore, February 2017.
17. "Introduction to Error Correcting Codes", Colloquium at IISER-Tirupati, February 2016.
18. Six lectures in Multilinear Algebra, NCM sponsored Instructional School for Teachers at SGGS Institute of Technology, Nanded, Maharashtra. December 2015.
19. "The MDS Conjecture and the Completeness of Rational Normal Curves over a finite field" at IISER Pune, September 2015.
20. "Grassmannians and Codes" at IISER Pune, June 2014.
21. "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.
22. "Symplectic Hodge-Lepage decomposition in positive characteristic" in the Novikov seminar at the Moscow State University, October 2013.
23. "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.
24. "Linear sections of Grassmann Varieties over finite fields" in the Conference "Current Trends in Algebra" held at IISER-Bhopal, August 2013.
25. AFS-3 held at Pune University, July 2013 : Lectures on differential geometry (connections on vector bundles)
26. "Weight spectrum of codes associated to the Grassmannian G(3,7)", Indian Institute of Science Education and Research Bhopal Jun 2012
27. "Algebraic-Geometric solutions of sine-Gordon equation: Topological charge", Tata Institute of Fundamental Research - CAM, Bangalore, Jun 2012.
28. "Linear Codes associated to Grassmann varieties", Indian Statistical Institute-Bangalore, Jun 2012.
29. "Automorphisms of Grassmann and related codes", Chennai Mathematical Institute, Jun 2012.
30. ATM school in Geometric Complex Analysis (Delhi Univ. March 2011) : 3 lectures
31. Workshop on Differential Geometry at CIMS Benaras Hindu University May 2011:
32. AFS-1 held at IISER Pune, December 2011 : 4 lectures on diffferential topology (degree theory and applications)