Two-tuple balance of non-binary sequences with ideal two-level autocorrelation

AbstractLet p be a prime, q=pm and Fq be the finite field with q elements. In this paper, we will consider q-ary sequences of period qn-1 for q>2 and study their various balance properties: symbol-balance, difference-balance, and two-tuple-balance properties. The array structure of the sequences is introduced, and various implications between these balance properties and the array structure are proved. Specifically, we prove that if a q-ary sequence of period qn-1 is difference-balanced and has the “cyclic” array structure then it is two-tuple-balanced. We conjecture that a difference-balanced q-ary sequence of period qn-1 must have the cyclic array structure. The conjecture is confirmed with respect to all of the known q-ary sequences which are difference-balanced, in particular, which have the ideal two-level autocorrelation function when q=p

Performance Assessment of Polyphase Sequences Using Cyclic Algorithm

Polyphase Sequences (known as P1, P2, Px, Frank) exist for a square integer length with good auto correlation properties are helpful in the several applications. Unlike the Barker and Binary Sequences which exist for certain length and exhibits a maximum of two digit merit factor. The Integrated Sidelobe level (ISL) is often used to define excellence of the autocorrelation properties of given Polyphase sequence. In this paper, we present the application of Cyclic Algorithm named CA which minimizes the ISL (Integrated Sidelobe Level) related metric which in turn improve the Merit factor to a greater extent is main thing in applications like RADAR, SONAR and communications. To illustrate the performance of the P1, P2, Px, Frank sequences when cyclic Algorithm is applied. we presented a number of examples for integer lengths. CA(Px) sequence exhibits the good Merit Factor among all the Polyphase sequences that are considered