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New perfect sequences of length \(2p\). (English) Zbl 0948.94006

Sixth International workshop on algebraic and combinatorial coding theory, ACCT-XI, Pskov, Russia, September 6-12, 1998. Proceedings. Moskva: Mezhdunarodnyj Tsentr Nauchnoj i Tekhnicheskoj Informatsii, 119-122 (1998).
From the introduction: “Let \(\mathbf x=(x_0,x_1,\dots,x_{n-1})\) be a complex-valued sequence of length \(n\) containing at least one nonzero component. The periodic autocorrelation function of \(\mathbf x\) is defined by \(R_{\mathbf x}(\tau):=\sum_{s=0}^{n-1}x_{s}x_{s+\tau}^{\ast}\), \(\tau =0,1,\dots,n-1\), where all indices are calculated \(\operatorname{mod} n\) and \(x^{\ast}\) denotes the complex conjugation of \(x\).
A sequence \(\mathbf x=(x_0,x_1,\dots,x_{n-1})\) is called a perfect sequence if and only if all the out-of-phase autocorrelation coefficients are equal to 0, i.e., \(R_{\mathbf x}(\tau)=0,\) \(\tau =0,1,\dots,n-1\).
The sequence \(\mathbf x=(x_0,x_1,\dots,x_n-1)\) is called a phase shift keyed (PSK) sequence if all components of the sequence lie on the unit circle.
New perfect PSK sequences are proposed of length \(2p\), where \(p\) is a prime integer.”.
For the entire collection see [Zbl 0918.00043].

MSC:

94A55 Shift register sequences and sequences over finite alphabets in information and communication theory
11B83 Special sequences and polynomials