Trace Representation of Legendre Sequences
Designs, Codes and Cryptography
Autocorrelation and Linear Complexity of the New Generalized Cyclotomic Sequences
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Sequences related to Legendre/Jacobi sequences
Information Sciences: an International Journal
Cryptographic properties of some binary generalized cyclotomic sequences with the length p2
Information Sciences: an International Journal
Some notes on prime-square sequences
Journal of Computer Science and Technology
Trace representation of some generalized cyclotomic sequences of length pq
Information Sciences: an International Journal
Linear complexity and autocorrelation of prime cube sequences
AAECC'07 Proceedings of the 17th international conference on Applied algebra, algebraic algorithms and error-correcting codes
Trace representation of Legendre sequences of Mersenne prime period
IEEE Transactions on Information Theory - Part 2
On the linear complexity of Legendre sequences
IEEE Transactions on Information Theory
On the linear complexity of Hall's sextic residue sequences
IEEE Transactions on Information Theory
New Generalized Cyclotomy and Its Applications
Finite Fields and Their Applications
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Let p be a prime with 6|(p-1) and integer m=1. As a generalization of the Hall's sextic residue sequences, we introduce some families of generalized cyclotomic binary sequences over the residue class ring modulo p^m by defining sextic generalized cyclotomic residue classes. We determine the values of the linear complexity, which are large enough to resist security attacks using the Berlekamp-Massey algorithm. We also investigate the trace function representation for the resulting sequences when m=2.