Nonexistence of Certain Almost p-ary Perfect Sequences
Sequences and Their Applications–SETA 2012: 7th International Conference …, 2012•Springer
… When m = p is a prime, in [2] the authors studied almost p-ary perfect sequences of period
n + 1. In particular, they determined the existence status of almost p-ary perfect sequences
of period n + 1 for 3 ≤ n ≤ 100, except some open cases (see Table 2 [2]). This open cases
lead the authors to their question (see Question 1 in [2]), that we quote: … We recall that if
p is prime and there exists an almost p-ary perfect sequence of period n + 1, then p|(n − 1)
(see Corollary 1 in [2], or Theorem 2 below). Hence, the condition p|(n − 1) in Question 1 is …
n + 1. In particular, they determined the existence status of almost p-ary perfect sequences
of period n + 1 for 3 ≤ n ≤ 100, except some open cases (see Table 2 [2]). This open cases
lead the authors to their question (see Question 1 in [2]), that we quote: … We recall that if
p is prime and there exists an almost p-ary perfect sequence of period n + 1, then p|(n − 1)
(see Corollary 1 in [2], or Theorem 2 below). Hence, the condition p|(n − 1) in Question 1 is …
Abstract
We prove nonexistence of almost p-ary perfect sequences of period n + 1, where n ∈ {50, 76, 94, 99, 100} and p is an odd prime dividing n − 1. This answers a question of Chee, Tan and Zhou.
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