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Abstract:
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A sequence a = (a0 ,a1 ,a2 , ... ,an) is said to be an almost p-ary sequence of period n + 1 if a0 = 0 and ai = (?p)bi for 1 = i = n, where ?p is a primitive p-th root of unity and bi ? {0, 1, . . . , p - 1}. Such a sequence a is called perfect if all its out-of-phase autocorrelation coefficients are zero. In the group G isomorphic to H1 × H2 where H1 and H2 are cyclic groups of order n + 1 and p respectively, it has been shown that a is perfect if and only if a subset R of G is an (n + 1, p, n, (n -1)/p) relative difference set relative to H2. Since almost p-ary perfect sequences are useful in some engineering applications, it is of interest to know whether or not, depending on the parameters n and p, a relative difference set R exists in G. We seek to establish the non- existence of such an R in several previously unresolved cases. |
