7 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…