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On the Minimum Linear Complexity of de Bruijn Sequences over Non-prime Finite Fields

✍ Scribed by Peter A. Hines

Publisher: Elsevier Science
Year: 1999
Tongue: English
Weight: 126 KB
Volume: 86
Category: Article
ISSN: 0097-3165
DOI: 10.1006/jcta.1998.2920

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✦ Synopsis

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.

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Characterising the Linear Complexity of Span 1 de Bruijn Sequences over Finite Fields

✍ Peter A. Hines 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 307 KB

We give a complete resolution to a conjecture regarding the characterisation of linear complexities of span 1 de Bruijn sequences over nonprime finite fields. This contrasts with results for prime fields, where the characterisation is equivalent to an open question concerning permutation polynomials