Special Classes of Set Codes and Their Applications

TL;DR

This work introduces generalized set codes, including set bicodes and set n-codes, with applications in cryptography, networking, and data storage, along with error detection and correction methods.

Contribution

The paper presents new classes of set codes, extending semigroup and group n-codes, with detailed definitions, examples, and potential applications in computer security and data management.

Findings

Defined various types of set n-codes.

Provided examples to illustrate concepts.

Discussed applications in cryptography and data storage.

Abstract

In this book, the authors introduce the notion of set codes, set bicodes and set n-codes. These are the most generalized notions of semigroup n-codes and group n-codes. Several types of set n-codes are defined. Several examples are given to enable the reader to understand the concept. These new classes of codes will find applications in cryptography, computer networking (where fragmenting of codes is to be carried out) and data storage (where confidentiality is to be maintained). We also describe the error detection and error correction of these codes. The authors feel that these codes would be appropriate to the computer dominated world. This book has three chapters. Chapter One gives basic concepts to make the book a self-contained one. In Chapter Two, the notion of set codes is introduced. The set bicodes and their generalization to set n-codes (n >= 3) is carried out in Chapter Three. This chapter also gives the applications of these codes in the above-mentioned fields.