On certain recurrent and automatic sequences in finite fields

Abstract : In this work we extend our study on a link between automaticity and certain algebraic power series over finite fields. Our starting point is a family of sequences in a finite field of characteristic $2$, recently introduced by the first author in connection with algebraic continued fractions. By including it in a large family of recurrent sequences in an arbitrary finite field, we prove its automaticity. Then we give a criterion on automatic sequences, generalizing a previous result and this allows us to present new families of automatic sequences in an arbitrary finite field.
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Submitted on : Monday, November 28, 2016 - 10:36:39 AM
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Alain Lasjaunias, Jia-Yan Yao. On certain recurrent and automatic sequences in finite fields. 10 pages. 2016. 〈hal-01313548〉

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