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SIAMDM

2010

2010

In this paper we study the problem of ﬁnding maximally sized subsets of binary strings (codes) of equal length that are immune to a given number r of repetitions, in the sense that no two strings in the code can give rise to the same string after r repetitions. We propose explicit number theoretic constructions of such subsets. In the case of r = 1 repetition, the proposed construction is asymptotically optimal. For r ≥ 1, the proposed construction is within a constant factor of the best known upper bound on the cardinality of a set of strings immune to r repetitions. Inspired by these constructions, we then develop a preﬁxing method for correcting any prescribed number r of repetition errors in an arbitrary binary linear block code. The proposed method constructs for each string in the given code a carefully chosen preﬁx such that the the resulting strings are all of the same length and such that despite up to any r repetitions in the concatenation of the preﬁx and the codew...

Added |
30 Jan 2011 |

Updated |
30 Jan 2011 |

Type |
Journal |

Year |
2010 |

Where |
SIAMDM |

Authors |
Lara Dolecek, Venkat Anantharam |

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