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Some z<sub>n-1</sub> terraces from z<sub>n</sub> power-sequences, n being an odd prime power

By I. Anderson and D.A. Preece

Abstract

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 &#8804; i &#8804; 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 &#60; n &#60; 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

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