SUMMARY This paper proposes a new multi-value sequence generated by utilizing primitive element, trace, and power residue symbol over odd characteristic finite field. In detail, let p and k be an odd prime number as the characteristic and a prime factor of p-1, respectively. Our proposal generates k-value sequence 'T = {1; I I; = fk(Tr(wi) +A)}, where w is a primitive element in the extension field 1Fpm, Tr(·) is the trace function that maps IF~ ___, 1Fp. A is a non-zero scalar in the prime field 1Fp, and !kO is a certain mapping function based on k-th power residue symbol. Thus, the proposed sequence has four parameters as p, m, k, and A.Then, this paper theoretically shows its period, autocorrelation, and cross-correlation. In addition, this paper discusses its linear complexity based on experimental results. Then, these features of the proposed sequence are observed with some examples.
In a related work REF , the authors considered a multivalued sequence and observed its period, autocorrelation, and cross-correlation as important properties.
A Multi-Value Sequence Generated by Power Residue Symbol and Trace Function over Odd Characteristic Field
IEICE Transactions
IEICE Transactions
Computer Science Mathematics