Numbers, Information and Complexity pp 21-27 | Cite as

# A Method to Estimate Partial-Period Correlations

## Abstract

Many applications require large families of sequences with good correlation properties. Some of the best families can be constructed by means of cyclic codes. The full-period correlation of such a family is closely connected with a complete sum of additive characters. In several important special cases it can be easily estimated. On the other hand, the partial period correlations, which are connected with certain incomplete sums of additive characters, are not easy to estimate. A device for estimating is the finite Fourier transform. This approach, which in fact is a modification of an old number theoretic method due to Vinogradov, needs bounds for hybrid sums of additive and multiplicative characters. In this survey we apply this approach in three cases: the *m*-sequence, the set of dual-BCH sequences, and the small Kasami set.

## Keywords

Code Word Cyclic Code Galois Ring Linear Binary Code Number Theoretic Method## Preview

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