Nonexistence of Certain Almost p-ary Perfect Sequences

Non-existence of Some Nearly Perfect Sequences, Near Butson–Hadamard Matrices, and Near Conference Matrices

“…We also want to thank Clemens Heuberger for several fruitful discussions on this topic during the special semester on Applications of Algebra and Number Theory held at the Johann Radon Institute for Computational and Applied Mathematics (RICAM) in Linz, October 14 -December 13, 2013. (v, m) γ = 0 (11, 9), (27,25), (35,33), (47,9), (59,57), (67,65), (71,69), (77,25), (79,77), (83,9), (83,27), (83,81), γ = 1 (6,3), (7,2), (7,4), (8,5), (11,2), (12,3), (12,9), (13,2), (13,5), (13,10),…”

“…In this paper we prove several new non-existence results on BH γ (v, m) and C γ (v, m) which can be interpreted as non-existence results for PS and NPS. For earlier non-existence results on PS and NPS see [3,6,7] and on Butson-Hadamard matrices [2,9].…”

Nearly perfect sequences with arbitrary out-of-phase autocorrelation

“…Therefore, an almost p-ary PS of period n + 1 exists when n is a prime power and p is a prime divisor of n − 1. By using Theorem 4 and results in [3,9] we obtain for n ≤ 100 that an almost p-ary PS of period n + 1 at all other cases do not exist except the undecided pairs (n, p) ∈ {(63, 31), (77, 19), (91, 3), (92, 7), (93, 23)}. In Section 5, we exclude the existence at the cases (n, p) ∈ {(63, 31), (91, 3), (92, 7), (93, 23)} by using multipliers.…”

“…In addition, we use the following result in proving the non-existence of RDS at certain values, see [1,Lemma 5.4] or [9,Proposition 1]. By using the method presented above and Lemma 4 we prove the following result.…”

“…Later Chee et al [3] extended the methods due to Ma and Ng [7] to almost p-ary nearly perfect sequences of types γ = 0 and γ = −1. Then, Özbudak et al [9] proved the non-existence of almost 2010 Mathematics subject classification. 05B10 94A55 p-ary perfect sequences at certain values.…”