Optimal Families of Perfect Polyphase Sequences from Cubic Polynomials

Min Kyu SONG  Hong-Yeop SONG  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E101-A   No.12   pp.2359-2365
Publication Date: 2018/12/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E101.A.2359
Type of Manuscript: Special Section PAPER (Special Section on Signal Design and Its Applications in Communications)
Category: Coding Theory
perfect polyphase sequences,  cubic polynomials,  optimal families of perfect polyphase sequences,  

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For an odd prime p and a positive integer k 2, we propose and analyze construction of perfect pk-ary sequences of period pk based on cubic polynomials over the integers modulo pk. The constructed perfect polyphase sequences from cubic polynomials is a subclass of the perfect polyphase sequences from the Mow's unified construction. And then, we give a general approach for constructing optimal families of perfect polyphase sequences with some properties of perfect polyphase sequences and their optimal families. By using this, we construct new optimal families of pk-ary perfect polyphase sequences of period pk. The constructed optimal families of perfect polyphase sequences are of size p-1.