It has been conjectured that over any non-prime finite field F p m and for any positive integer n, there exists a span n de Bruijn sequence over F p m which has the minimum possible linear complexity p nm&1 +n. We give a proof by construction that this conjecture is true.
On the complexity of the normal bases via prime Gauss period over finite fields
โ Scribed by Qunying Liao; Keqin Feng
- Book ID
- 107347131
- Publisher
- Academy of Mathematics and Systems Science, Chinese Academy of Sciences
- Year
- 2009
- Tongue
- English
- Weight
- 271 KB
- Volume
- 22
- Category
- Article
- ISSN
- 1009-6124
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๐ SIMILAR VOLUMES
## Let % O L denote the "nite "eld with qL elements, for q a prime power. % O L may be regarded as an n-dimensional vector space over % O . 3% O L generates a normal basis for this vector space (% O L :% O ), if + , O, q , 2 , O L\ , are linearly independent over % O . Let N O (n) denote the numbe
The number of points on the curve aY e =bX e +c (abc{0) defined over a finite field F q , q#1 (mod e), is known to be obtainable in terms of Jacobi sums and cyclotomic numbers of order e with respect to this field. In this paper, we obtain explicitly the Jacobi sums and cyclotomic numbers of order e