Paper Info

Title | ||
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Correctable errors of weight half the minimum distance plus one for the first-order Reed-muller codes |

Abstract | ||
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The number of correctable/uncorrectable errors of weight half the minimum distance plus one for the first-order Reed-Muller codes is determined. From a cryptographic viewpoint, this result immediately leads to the exact number of Boolean functions of m variables with nonlinearity 2(m-2) + 1. The notion of larger half and trial set, which is introduced by Helleseth, Klove, and Levenshtein to describe the monotone structure of correctable/uncorrectable errors, plays a significant role in the result. |

Year | DOI | Venue |
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2007 | 10.1007/978-3-540-77224-8_15 | international symposium on information theory |

Keywords | Field | DocType |

minimum distance,correctable error,weight half,first-order reed-muller code,boolean function,reed muller code,first order | Boolean function,Discrete mathematics,Combinatorics,Nonlinear system,Cryptography,First order,Reed–Muller code,Mathematics,Monotone polygon | Conference |

Volume | ISSN | ISBN |

4851 | 0302-9743 | 3-540-77223-5 |

Citations | PageRank | References |

0 | 0.34 | 7 |

Authors | ||

2 |

Authors (2 rows)

Cited by (0 rows)

References (7 rows)

Name | Order | Citations | PageRank |
---|---|---|---|

Kenji Yasunaga | 1 | 18 | 7.52 |

Toru Fujiwara | 2 | 63 | 16.94 |