## New Classes of Codes for Cryptologists and Computer ScientistsIn this book, new classes of codes are introduced to help cryptologists and computer scientists.These codes will find application in networking and data storage.Further, these new classes of codes cannot be easily cracked by hackers, so they will be useful in defense departments. |

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### Contents

7 | |

12 Bimatrices and their Generalizations | 33 |

BICODES AND THEIR GENERALIZATIONS | 45 |

22 Error Detection and Error Correction in ncodes n 2 | 103 |

23 False nmatrix and Pseudo False nmatrix | 137 |

24 False ncodes n 2 | 156 |

PERIYAR LINEAR CODES | 169 |

32 Application of these New Classes of Codes | 193 |

195 | |

199 | |

ABOUT THE AUTHORS | 206 |

### Common terms and phrases

1-pseudo biapproximation bimatrix H bivector C2 J C3 check symbols classes of codes Clearly code of length code words coding theory correct message coset leader cyclic bicode cyclic code decoding define the notion DEFINITION dual duo P-linear code error false bicode false mixed finite field following example G2 J G3 given by G Hamming code Hamming distance Hj u H2 illustrate inner product space Let H Let us consider lj C2 lj G2 lj H2 lj x2 M2 u M3 matrix H message symbols mixed false n-approximation n-code word n-subspace n-vector orthogonal code orthogonal tricode P-cyclic parity check bimatrix parity check code Periyar linear code polynomial pseudo best approximation pseudo false pseudo inner product received message rectangular matrix repetition bicode repetition code square matrix subcode of length subspace trimatrix G vector space weak P-linear code yi uy2 yj C2