Anuradha S. Garge

activity

20122026

collaborators

8 papers

cs.IT2026

Suslin-Rao Codes : the bridge between pure and applied

Nitin Kenjale, Anuradha S. Garge

In the year $1977,$ while developing the theory of modules arising in the context of Serre's problem on projective modules in the paper ``On Stably Free Modules" (see \cite{AS}), A…

math.RA2026

Matrices over non-commutative rings as sums of fifth and seventh powers

Tanay Kochrekar, A. S. Garge

Let $R$ be non-commutative ring with unity. In this paper, we prove that a given matrix in $M_{n} (R)$ is a sum of $p$ -th powers in $M_{n} (R)$ , where $n < p$ if and only if its trace ca…

math.NT2026

Integral quadratic forms over a ring of $p$ -adic integers

Mrunal Hardikar, Anuradha S. Garge

Jungin Lee in 2018 proved a necessary and sufficient condition that an integral quadratic form $\sum_{i = 1}^{m} a_{i} X_{i}^{2}$ is universal over $M_{2} (Z)$ . For a positive integer…

cs.IT2026

On the Algebraic Structure Underlying the Support Enumerators of Linear Codes

Nitin Kenjale, Anuradha S. Garge

In this paper, we have introduced the concepts of support distribution and the support enumerator as refinements of the classical weight distribution and weight enumerator respecti…

math.NT2020

Trace and discriminant criteria for a matrix to be a sum of sixth and eighth powers of matrices

Rakesh Barai, Anuradha S. Garge

In this paper, we shall be considering the Waring's problem for matrices. One version of the problem involves writing an $n \times n$ matrix over a commutative ring $R$ with unity…

math.NT2020

Representation of two by two matrices over perfect fields by a diagonal quadratic form

Murtuza Nullwala, Anuradha S. Garge

Let F be a perfect field. Then the diagonal quadratic form $a_{i} X_{i}^{2}$ over $F$ is universal over $M_{2} (F)$ if and only if atleast two of the $a_{i}$ are non-zero.

math.KT2013

Global actions, K-theory and unimodular rows

Anthony Bak, Anuradha S. Garge

Global actions were introduced by Bak in order to have a homotopy theory in a purely algebraic setting. In this paper we apply his techniques in a particular case: the (single doma…

math.KT2012

A nice group structure on the orbit space of unimodular rows-II

Anjan Gupta, Anuradha Garge, Ravi A. Rao

We establish an Excision type theorem for niceness of group structure on the orbit space of unimodular rows of length $n$ modulo elementary action. This permits us to establish nic…