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, Finite Geometry, Combinatorics

Preprints:

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

Twisted Jacquet modules associated to maximal parabolic subgroups and cuspidal representations of GL_n(q) (with Kumar Balasubramanian, and Himanshi Khurana), arXiv

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