## Fundamentals of Error-Correcting CodesFundamentals of Error Correcting Codes is an in-depth introduction to coding theory from both an engineering and mathematical viewpoint. As well as covering classical topics, much coverage is included of recent techniques which until now could only be found in specialist journals and book publications. Numerous exercises and examples and an accessible writing style make this a lucid and effective introduction to coding theory for advanced undergraduate and graduate students, researchers and engineers, whether approaching the subject from a mathematical, engineering or computer science background. |

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### Contents

Basic concepts of linear codes | 1 |

Bounds On the Size of COdes | 53 |

Finite fields | 100 |

Cyclic codes | 121 |

BCH and ReedSolomon COdes | 168 |

Duadic Codes | 209 |

Weight distributions | 252 |

Designs | 291 |

Some favorite Selfdual COdes | 397 |

Covering radius and cosets | 432 |

Codes over Z4 | 467 |

Codes from algebraic geometry | 517 |

Convolutional COdes | 546 |

Soft decision and iterative decoding | 573 |

References 615 | 596 |

Selfdual Codes | 338 |

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### Common terms and phrases

Ag(n assume Asymptotic BCH codes binary Golay code blocks C1 and C2 code of length code over F codewords codewords of weight columns compute construction contains convolutional code coordinates Corollary coset leader cosets modulo cosets of weight covering radius cyclic code defining set degree denoted dimension divisor doubly-even elements of F encoder entries equations equivalent errors even-like Example Exercise exist following hold formally self-dual given gives Hamming code hence Hermitian hexacode idempotent implying inner product integer irreducible polynomials lattice Lemma linear code matrix G minimum distance minimum weight multiple nonzero obtained orthogonal parity check matrix PAut(C permutation points primitive projective plane Proof punctured QR codes quadratic residue codes received vector Reed–Solomon codes Section self-dual binary codes self-dual codes self-orthogonal Show subcode Suppose syndrome Table ternary Golay code trellis Type II codes unique upper bound Verify weight codewords weight distribution weight enumerator wt(x zero