Auto and Cross Correlation of Well Balanced Sequence over Odd Characteristic Field

Abstract

In this paper, the authors have proposed a new approach for generating multi-value sequence by utilizing primitive element, trace function, and k-th power residue symbol over odd characteristic field. Let p be an odd prime and Fp be an odd characteristic prime field, m be the degree of the primitive polynomial f(x), and k be a prime factor of p-1. In details, the procedure for generating multi-value sequence is as follows: primitive polynomial f(x) generates maximum length vector sequence, then trace function Tr(.) maps an element of extension field Fpm to an element of prime field Fp, next non-zero scalar A 2 Fp is added to the trace value, and finally k-th power residue symbol is utilized to map the scalars into (k + 1) values multi-value sequence. In this method, a certain mapping function Mk(.) is utilized during the autocorrelation calculation. Hence, our proposed multi-value sequence has some parameters such as p, m, k, and A. This paper discusses the period, autocorrelation, and cross-correlation properties of proposed multi-value sequence based on some experimental results.