Some da capo directed power-sequence Z n + 1 terraces with n an odd prime power
2007; Elsevier BV; Volume: 308; Issue: 2-3 Linguagem: Inglês
10.1016/j.disc.2006.11.033
ISSN1872-681X
Autores Tópico(s)Coding theory and cryptography
ResumoA terrace for Zn is a particular type of sequence formed from the n elements of Zn. For n odd, many procedures are available for constructing power-sequence terraces for Zn; each such terrace may be partitioned into segments one of which contains merely the zero element of Zn, whereas each other segment is either (a) a sequence of successive powers of a non-zero element of Zn or (b) such a sequence multiplied throughout by a constant. We now extend this idea by using power-sequences in Zn to produce some terraces for Zn+1 where n is an odd prime power satisfying n≡1 or 3 (mod 8). Each terrace now consists of a sequence of segments, one containing merely the element 0 and another merely containing the element n, the remaining segments each being of type (a) or (b) above with each of its distinct entries i from Zn⧹{0} evaluated so that 1⩽i⩽n-1. The terraces constructed are da capo directed terraces, i.e. each terrace (a1,a2,…,an+1) has ai-ai-1=-(ai+m-ai-1+m) for all i satisfying 2≤i≤m where m=(n+1)/2.
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