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Information Theory, Coding and Cryptography by Mandal, Nilotpal Manna, Arijit Saha

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Chapter 5

Linear Block Codes

5.1  INTRODUCTION

With the advent of digital computers and digital data communication systems, information is coded in binary digits ‘0’ or ‘1’. This binary information sequence is segmented into message blocks of fixed length in block coding. Each message block consists of k-information bits and is denoted by u. Thus, there may be 2k distinct messages. According to certain rules, this message u is then transformed into a binary n-tuple v, with n > k. The binary n-tuple v is referred to as the code vector (or code word) of the message u. Thus, there may be 2k distinct code vectors corresponding to 2k distinct possible message vectors. The set of these 2k distinct code vectors is known as block code. A desirable property ...

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