10 papers
Two Families of Linear Codes Containing Non-GRS MDS Codes
Kanat Abdukhalikov, Gyanendra K. Verma
We construct two new families of linear codes by modifying the generator matrices of generalized Reed-Solomon (GRS) codes. For these codes, we explicitly derive parity-check matric…
On Function-Correcting Codes in the Lee Metric
Gyanendra K. Verma, Abhay Kumar Singh
Function-correcting codes are a coding framework designed to minimize redundancy while ensuring that specific functions or computations of encoded data can be reliably recovered, e…
Some constructions of non-generalized Reed-Solomon MDS Codes
Kanat Abdukhalikov, Cunsheng Ding, Gyanendra K. Verma
We investigate two classes of extended codes and provide necessary and sufficient conditions for these codes to be non-GRS MDS codes. We also determine the parity check matrices fo…
Function-Correcting -symbol Codes for Locally -Functions
Gyanendra K. Verma, Anamika Singh, Abhay Kumar Singh
The family of functions plays a central role in the design and effectiveness of function-correcting codes. By focusing on a well-defined family of functions, function-correcting co…
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…
Linear Complementary Pairs of Quasi-Cyclic and Quasi-Twisted Codes
Kanat Abdukhalikov, Duy Ho, San Ling +1
In this paper, we provide a polynomial characterization of linear complementary pairs of quasi-cyclic and quasi-twisted codes of index 2. We also give several examples of linear co…
Linear complementary dual quasi-cyclic codes of index 2
Kanat Abdukhalikov, Duy Ho, San Ling +1
We provide a polynomial approach to investigate linear complementary dual (LCD) quasi-cyclic codes over finite fields. We establish necessary and sufficient conditions for LCD quas…
Construction of Additive Complementary Dual Codes Over Finite Fields
Gyanendra K. Verma, R. K. Sharma
In this work, we investigate additive complementary dual (ACD) codes and their construction over finite fields with respect to the trace inner products, where $q…
Construction Methods for Galois LCD codes over Finite Fields
Gyanendra K. Verma, Astha Agrawal, R. K. Sharma
In this article, first we present a method for constructing many Hermitian LCD codes from a given Hermitian LCD code, and then provide several methods which utilize either a given…
Galois LCD Codes Over Fq + uFq + vFq + uvFq
Astha Agrawal, Gyanendra K. Verma, R. K. Sharma
In \cite{anote}, Wu and Shi studied -Galois LCD codes over finite chain ring , where and for some prime and positi…