Finite field for scientists and engineers
Finite field for scientists and engineers
Spread spectrum communications handbook (revised ed.)
Spread spectrum communications handbook (revised ed.)
Shift Register Sequences
Signal Design for Good Correlation: For Wireless Communication, Cryptography, and Radar
Signal Design for Good Correlation: For Wireless Communication, Cryptography, and Radar
New Cyclic Difference Sets with Singer Parameters Constructed from d-Homogeneous Functions
Designs, Codes and Cryptography
IEEE Transactions on Information Theory
New nonbinary sequences with ideal two-level autocorrelation
IEEE Transactions on Information Theory
d-form sequences: families of sequences with low correlation values and large linear spans
IEEE Transactions on Information Theory
| Hi-index | 0.05 |
Let 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.