Spring 2004

Computational Problems

Basics | Sets, lists, linear algebra, computation in the integers. |

Algebraic integers | Extension of the integers by the root of a polynomial. |

Modular Arithmetic | Polynomials and matrices mod n. |

Finite Fields | Constructing and doing arithmetic in finite fields. |

Integers | Basic computations in the integers. | |

Polynomial Rings | Polynomial rings, their quotients, evaluation of polynomials. | |

Finite Fields | Finite field and their extensions. | |

Reed-Solomon Codes | Constructing the generator and check matrices, systematic encoding. | |

Decoding of Reed-Solomon Codes | The Berlekamp-Massey algorithm, and computation of the error values using Sec 8. |