New Classes of Codes for Cryptologists and Computer Scientists

TL;DR

This book introduces new classes of error-correcting codes designed for cryptography and secure communication, emphasizing ease of understanding and innovative security features like misleading intruders.

Contribution

It presents novel code classes such as bicodes, n-codes, and Periyar linear codes, with new error detection and correction methods, and aims to make coding theory accessible without advanced mathematics.

Findings

Introduction of bicodes, n-codes, and Periyar linear codes.

New error detection and correction methods using pseudo best n-approximations.

Codes designed to mislead intruders and enhance security.

Abstract

In this book, we have introduced several new classes of codes to aid cryptologists and computer scientists. We have explained these codes very non-technically so that a strong mathematical foundation is not needed to understand them. This book also provides an easy method to detect and correct errors that occur during transmission. Further, some of the codes are constructed so as to mislead an intruder/ hacker. False n-codes, whole n-codes can serve this pupose. These codes can be used to ensure security in networks and safe transmission of identity. We have named a few new classes of codes after Periyar, the south-Indian social leader, to mark his services to humanity. This book is divided into three chapters. Chapter one is introductory in nature. The notion of bicodes and their generalization, and n-codes are introduced in the second chapter. Periyar linear codes are introduced in the third chapter. We have used two methods, viz. pseudo best n-approximations and n-coset leader properties to detect and correct errors.