On certain recurrent and automatic sequences in finite fieldsReport as inadecuate




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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.





Author: Alain Lasjaunias - Jia-Yan Yao -

Source: https://hal.archives-ouvertes.fr/



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