Optimal Families of Perfect Polyphase Sequences From the Array Structure of Fermat-Quotient Sequences

—We show that a p-ary polyphase sequence of period p2 from the Fermat quotients is perfect. That is, its periodic autocorrelation is zero for all non-trivial phase shifts. We call this Fermat-quotient sequence. We propose a collection of optimal families of perfect polyphase sequences using the Fermatquotient sequences in the sense of the Sarwate bound. That is, the cross correlation of two members in a family is upper bounded by p. To investigate some relation between Fermat-quotient sequences and Frank–Zadoff sequences and to construct optimal families including these sequences, we introduce generators of p-ary polyphase sequences of period p2 using their p × p array structures. We call an optimal generator to be the generator of some p-ary polyphase sequences which are perfect and which gives an optimal family by the proposed construction. Finally, we propose an algebraic construction for optimal generators as another main result. A lot of optimal families of size p − 1 can b...

• Type: Journal
• Year: 2016
• Where: TIT
• Authors: Ki-Hyeon Park, Hong-Yeop Song, Dae San Kim, Solomon W. Golomb
• Keywords: Education, TIT 2016