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A terrace for Z<sub>m</sub> is a particular type of sequence formed from the m elements of Z<sub>m</sub>. For m\ud odd, many procedures are available for constructing power-sequence terraces for Z<sub>m</sub>; each terrace of this\ud sort may be partitioned into segments, of which one contains merely the zero element of Z<sub>m</sub>, whereas\ud every other segment is either a sequence of successive powers of an element of Z<sub>m</sub> or such a sequence\ud multiplied throughout by a constant. We now refine this idea to show that, for m=n−1, where n is an odd prime power, there are many ways in which power-sequences in Z<sub>n</sub> can be used to arrange the elements of Z<sub>n</sub> \ {0} in a sequence of distinct entries i, 1 ≤ i ≤ m, usually in two or more segments, which becomes a terrace for Z<sub>m</sub> when interpreted modulo m instead of modulo n. Our constructions provide terraces for Z<sub>n-1</sub> for all prime powers n satisfying 0 < n < 300 except for n = 125, 127 and 257

Topics:
QA

Publisher: Cambridge University Press

Year: 2007

OAI identifier:
oai:eprints.gla.ac.uk:12984

Provided by:
Enlighten

Downloaded from
http://eprints.gla.ac.uk/12984/1/12984.pdf

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