Rati Ludhani

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20212026

most citedOn the Minimum Distance, Minimum Weight Codewords, and the Dimension of Projective Reed-Muller Codes

11 citations · 14 across the 6 of their papers we have counts for

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math.AC2024

Projective Nullstellensatz for not necessarily algebraically closed fields

Rati Ludhani

The Nullstellensatz, proved by Hilbert in 1893, is a classical result that holds when the base field is algebraically closed. When the base field is finite, a version of Hilbert's…

math.CO2024

Betti Numbers and Higher Weight Spectra of Reed-Muller Codes $R M_{q} (2, 2)$

Sudhir R. Ghorpade, Trygve Johnsen, Rati Ludhani +1

We determine all the Betti numbers of the $q$ -ary second order Reed-Muller codes of length $q^{2}$ , and also of the elongations of matroids associated to these codes. We then use it…

Projective Nullstellensatz for not necessarily algebraically closed fields

Betti Numbers and Higher Weight Spectra of Reed-Muller Codes RMq​(2,2)

Betti Numbers and Higher Weight Spectra of Reed-Muller Codes $R M_{q} (2, 2)$