arXiv subjects

Nikita Jain

Publications and source records attributed to Nikita Jain.

4 recordsLinked to original sources

arXiv2024

On constacyclic codes over a class of non-chain rings

In this paper, a unique form of generators of a constacyclic code of arbitrary length over a non-chain ring of the type $\mathtt{R_{_θ}}=Z_{4}+νZ_{4}, ν^{2}=θ\in Z_{4}+νZ_{4}$ has been obtained. Further, rank and cardinality of a constacyclic code of arbitrary length over a non-chain ring of the type $\mathtt{R_{_θ}}$ have been obtained by determining a minimal spanning set of the code. Also, necessary and sufficient conditions for a constacyclic code of arbitrary length over a non-chain ring of the type $\mathtt{R_{_θ}}$ to be reversible have been determined. Examples have also been presented in support of our results.

math.AC↗

arXiv2023

Reversible and Reversible Complement Cyclic codes over a class of non-chain rings

In this paper, necessary and sufficient conditions for a cyclic code of arbitrary length over the non-chain rings $Z_{4}+νZ_{4}$ for $ν^{2} \in \{0,1,ν,2ν,3ν,2+ν,2+3ν,3+2ν\}$ to be a reversible cyclic code have been established. Also, conditions for a cyclic code over these non-chain rings to be a reversible complement cyclic code which are necessary as well as sufficient have been determined. Some examples of reversible and reversible complement cyclic codes over these rings have also been presented.

cs.IT↗

arXiv2023

Structure and Rank of Cyclic codes over a class of non-chain rings

The rings $Z_{4}+νZ_{4}$ have been classified into chain rings and non-chain rings on the basis of the values of $ν^{2} \in Z_{4}+νZ_{4}.$ In this paper, the structure of cyclic codes of arbitrary length over the rings $Z_{4}+νZ_{4}$ for those values of $ν^{2}$ for which these are non-chain rings has been established. A unique form of generators of these codes has also been obtained. Further, rank and cardinality of these codes have been established by finding minimal spanning sets for these codes.

cs.IT↗

arXiv2016

E3 : Keyphrase based News Event Exploration Engine

This paper presents a novel system E3 for extracting keyphrases from news content for the purpose of offering the news audience a broad overview of news events, with especially high content volume. Given an input query, E3 extracts keyphrases and enrich them by tagging, ranking and finding role for frequently associated keyphrases. Also, E3 finds the novelty and activeness of keyphrases using news publication date, to identify the most interesting and informative keyphrases.

cs.IR↗