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A formula on linear complexity of highest coordinate sequences from maximal periodic sequences over Galois rings. (English) Zbl 1146.11061

Summary: Using a polynomial expression of the highest coordinate map, we deduce an exact formula on the linear complexity of the highest coordinate sequence derived from a maximal periodic sequence over an arbitrary Galois ring of characteristic \(p^2\), where \(p\) is a prime. This generalizes the known result of P. Udaya and M. U. Siddiqi [IEEE Trans. Inf. Theory 42, No. 1, 206–216 (1996; Zbl 0851.94016)] for the case that the Galois ring is \(\mathbb Z_4\).

MSC:

11Y16 Number-theoretic algorithms; complexity
11T30 Structure theory for finite fields and commutative rings (number-theoretic aspects)
94A60 Cryptography

Citations:

Zbl 0851.94016
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