9 papers
Equality and iso-duality of Generalized Geometric Goppa codes
Jyoti Dasgupta, Nupur Patanker
Geometric Goppa codes are constructed by evaluating elements of an algebraic function field at the places of degree one. Extending this, generalized geometric Goppa codes were defi…
Code size constraints in b-symbol read channels: A bound analysis
Gyanendra K. Verma, Nupur Patanker, Abhay Kumar Singh
In classical coding theory, error-correcting codes are designed to protect against errors occurring at individual symbol positions in a codeword. However, in practical storage and…
On the number of minimal and next-to-minimal weight codewords of toric codes over hypersimplices
Cícero Carvalho, Nupur Patanker
Toric codes are a type of evaluation code introduced by J.P. Hansen in 2000. They are produced by evaluating (a vector space composed by) polynomials at the points of $(\mathbb{F}_…
Next-to-minimal weight of toric codes defined over hypersimplices
Cícero Carvalho, Nupur Patanker
Toric codes are a type of evaluation codes introduced by J.P. Hansen in 2000. They are produced by evaluating (a vector space composed by) polynomials at the points of $(\mathbb{F}…
Codeword Stabilized Codes from m-Uniform Graph States
Sowrabh Sudevan, Sourin Das, Thamadathil Aswanth +2
An m-uniform quantum state on n qubits is an entangled state in which every m-qubit subsystem is maximally mixed. Starting with an m-uniform state realized as the graph state assoc…
Generalization of trace codes to places of higher degree
Nupur Patanker, Sanjay Kumar Singh
In this note, we give a construction of codes on algebraic function field using places of (not necessarily of degree one) and trace functions from various e…
Generalized Hamming weights of toric codes over hypersimplices and square-free affine evaluation codes
Nupur Patanker, Sanjay Kumar Singh
Let be a finite field with elements, where is a power of prime . A polynomial over is square-free if all its monomials are square-free.…
On geometric Goppa codes from Elementary Abelian -Extensions of
Nupur Patanker, Sanjay Kumar Singh
Let be a prime number and an integer. In this short note, we investigate one-point geometric Goppa codes associated with an elementary abelian -extension of $\mathbb{…
A Short Note on Self-Duality of Goppa Codes on Elliptic and Hyperelliptic Function Fields
Nupur Patanker, Sanjay Kumar Singh
In this note, we investigate Goppa codes which are constructed by means of Elliptic function field and Hyperelliptic function field. We also give a simple criterion for self-dualit…