### Abstract

We classify some p^{k}-ary (p prime, k integer) generalized m-sequences and generalized Gordon-Mills-Welch (GMW) sequences of period p^{2k} - 1 over a residue class ring R = GF (p [ξ⌉/(ξ^{k}) having optimal partial Hamming autocorrelation properties. In frequency hopping (FH) spread-spectrum systems, these sequences are useful for synchronizing process. Suppose, for example, that a transmitting p^{k}-ary FH patterns of period p^{2k} - 1 are correlated at a receiver. Usually, the length of a correlation window, denoted by L, is shorter than the pattern's overall period. In that case, the maximum value of the out-of-phase Hamming autocorrelation is lower-bounded by ⌈^{L}/p^{k} + 1⌉ but the classified sequences achieve this bound with equality for any positive integer L.

Original language | English |
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Pages (from-to) | 2438-2442 |

Number of pages | 5 |

Journal | IEEE Transactions on Information Theory |

Volume | 50 |

Issue number | 10 |

DOIs | |

Publication status | Published - 2004 Oct 1 |

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### All Science Journal Classification (ASJC) codes

- Information Systems
- Computer Science Applications
- Library and Information Sciences

### Cite this

*IEEE Transactions on Information Theory*,

*50*(10), 2438-2442. https://doi.org/10.1109/TIT.2004.834792