Research Projects

Modern data-driven ecosystems, such as cloud computing platforms, distributed databases, and edge storage networks, demand highly reliable and efficient data redundancy strategies. Node failures in DSS are inevitable, and ensuring seamless data recovery with minimal overhead is a pressing concern. In response to this challenge, FRCs have emerged as a promising coding paradigm. They facilitate exact, uncoded repairs with minimum repair bandwidth, while being significantly simpler to implement than traditional regenerating codes. A compelling synergy has been discovered between $t$-designs, and the construction of FRCs. $t$-Designs not only endow the codes with elegant combinatorial properties but also enhance their performance in terms of failure tolerance, repair flexibility, and parallel data access. This project seeks to harness the power of 2-designs and 3-designs, especially those derived from o-polynomials and affine geometries, to build a new generation of universally good, optimal, and flexible FRCs. In a communication system, data are transmitted from a sender to a receiver via a channel. This channel is often affected by many sources of noise and interference, which may damage the data during transmission. Typically, removing the error is not an option. In fact, the only efficient solution is to make the data noise-proof, which can be achieved by adding redundancy. Coding theory keeps the expense of additional redundancy under control by using efficient coding tools that also allow effective decoding methods. Linear codes have been in use in communication systems and data storage in daily life. We are interested in codes with large minimum Hamming distance and small length. High minimum distance and small length are controversial goals for the optimization of codes. A distance optimal code has the highest possible error-detecting as well as error-correcting capacity for a given code length and code size. Due to this reason, the study of distance optimal codes has received huge attention in recent years. Secret sharing schemes are becoming essential nowadays; in fact, these are used heavily in electronic voting systems, cryptographic protocols, banking systems, etc. Minimal linear codes have interesting applications in secret sharing schemes and secure two-party computation. When the dimension of the hull of a linear code is small, it is considered useful from an application point of view. Due to this reason, the linear codes with zero- and one-dimension hull are extensively studied in recent past. If the hull of a linear code is trivial then it is called an LCD code. LCD codes are important linear codes due to their use in implementations against side-channel attacks and fault injection attacks. Thus, it is of great interest to construct and investigate linear codes which have many applications. Motivated by the above, in this project I will investigate linear codes which have nice algebraic structures and have good parameters.