Journal ArticleDOI
Perfect Gaussian Integer Sequences of Odd Prime Length
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TLDR
For any odd prime p, using the cyclotomic classes of order 2 and 4 with respect to GF(p), the perfect and odd perfect Gaussian integer sequences of length p are proposed.Abstract:
A Gaussian integer is a complex number whose real and imaginary parts are both integers. A Gaussian integer sequence is called perfect (odd perfect) if the out-of-phase values of the periodic (odd periodic) autocorrelation function are equal to zero. In this letter, for any odd prime p, using the cyclotomic classes of order 2 and 4 with respect to GF(p), we propose perfect and odd perfect Gaussian integer sequences of length p. Several examples are also given.read more
Citations
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Perfect Gaussian Integer Sequences of Arbitrary Length
Soo-Chang Pei,Kuo-Wei Chang +1 more
TL;DR: This work describes some methods to generate zero autocorrelation Gauss integer sequences of arbitrary length that can be combined with each other so that more choices can be made.
Journal ArticleDOI
New Perfect Gaussian Integer Sequences of Period pq
TL;DR: In this letter, by using Whiteman's generalized cyclotomy of order 2 over ℤ pq, where p,q are twin primes, new perfect Gaussian integer sequences of period pq are constructed.
Journal ArticleDOI
Perfect Gaussian Integer Sequences of Arbitrary Composite Length
TL;DR: This paper proposes a method for constructing degree-3 and degree-4 perfect Gaussian integer sequences (PGISs) of an arbitrary composite length utilizing an upsampling technique and the base sequence concept proposed by Hu, Wang, and Li.
Journal ArticleDOI
Perfect Gaussian Integer Sequences of Odd Period ${2^m} - 1$
TL;DR: In this letter, some perfect Gaussian integer sequences of period 2m - 1 are proposed based on the trace representations of Legendre sequences, Hall's sextic residue sequences, m-sequences, and Gordon-Mills-Welch (GMW) sequences over the finite field \BBF2m.
Journal ArticleDOI
A Systematic Method for Constructing Sparse Gaussian Integer Sequences With Ideal Periodic Autocorrelation Functions
TL;DR: A method for constructing sparse perfect Gaussian integer sequences (SPGIS) in which most of the sequence elements are zero, and a systematic investigation is performed into the properties of the SPGISs and their Fourier dual equivalents.
References
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Journal ArticleDOI
Crosscorrelation properties of pseudorandom and related sequences
TL;DR: This paper presents a survey of recent results and provides several new results on the periodic and aperiodic crosscorrelation functions for pairs of m-sequences and for Pair of related (but not maximal-length) binary shift register sequences.
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Polyphase codes with good periodic correlation properties (Corresp.)
TL;DR: This correspondence describes the construction of complex codes of the form exp i \alpha_k whose discrete circular autocorrelations are zero for all nonzero lags.
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Polyphase codes with good nonperiodic correlation properties
TL;DR: N -phase Codes are described which have an autocorrelation function with one main peak and very small side peaks and doppler shift effects appear to be similar to those of linear FM radar pulse compression.
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Phase shift pulse codes with good periodic correlation properties
TL;DR: A method of generating phase shift pulse codes of arbitrarily long length with zero periodic correlation except for the peak for zero shift is presented.