On the Aperiodic Correlation Function of Galois Ring m-Sequences

Authors:
P. Udaya;Serdar Boztas
Affiliations:
-;-
Venue:
AAECC-14 Proceedings of the 14th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
Year:
2001

Citing 5
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Abstract

We define Gauss-like sums over the Galois Ring GR(4, r) and bound them using the Cauchy-Schwarz inequality. These sums are then used to obtain an upper bound on the aperiodic correlation function of quadriphase m-sequences constructed from GR(4, r).Our first bound 驴1 has a simple derivation and is better than the previous upper bound of Shanbag et. al. for small values of N. We then make use of a result of Shanbag et. al. to improve our bound which gives rise to a bound 驴improved which is better than the bound of Shanbag et. al.These results can be used as a benchmark while searching for the best phases--termed auto-optimal phases--of such quadriphase sequences for use in spread spectrum communication systems. The bounds can also be applied to many other classes of non binary sequences.