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

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Chapter 6

Cyclic Codes

6.1  INTRODUCTION

Cyclic code is a subclass of linear codes. Any cyclic shift of a code word results in another valid code. This feature allows easy implementation of encoding as well as syndrome computation with linear sequential circuits by employing shift registers and feedback connections. Since it possesses considerable amount of algebra inherently, there are many practical methods of decoding. Random error correction and burst error correction are possible to the large extent due to involvement of algebra. The theory of Galois field can be used effectively to study and analyze new cyclic codes.

6.2  GENERATION

If a set of n-components v = (v0,v1,v2,...,vn 1) is cyclically shifted one place to right, another set ...

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