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ON LINEARISED POLYNOMIALS, SIDON ARRAYS AND FAST CONSTRUCTION OF SIDON SETS

Part of: Finite fields and commutative rings (number-theoretic aspects) Sequences and sets

Published online by Cambridge University Press:  30 August 2022

CESAR ANDRADE Open the ORCID record for CESAR ANDRADE [Opens in a new window] ,
YAMIDT BERMUDEZ Open the ORCID record for YAMIDT BERMUDEZ [Opens in a new window]  and
CARLOS TRUJILLO Open the ORCID record for CARLOS TRUJILLO [Opens in a new window]
CESAR ANDRADE
Affiliation:
Departamento de Matemáticas, Universidad del Valle, Cali, Colombia e-mail: cesar.andrade@correounivalle.edu.co
YAMIDT BERMUDEZ*
Affiliation:
Departamento de Matemáticas, Universidad del Valle, Cali, Colombia
CARLOS TRUJILLO
Affiliation:
Departamento de Matemáticas, Universidad del Cauca, Popayan, Colombia e-mail: trujillo@unicauca.edu.co
*
e-mail: yamidt.bermudez@correounivalle.edu.co
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Abstract

A Sidon set is a subset of an Abelian group with the property that the sums of two distinct elements are distinct. We relate the Sidon sets constructed by Bose to affine subspaces of $ \mathbb {F} _ {q ^ 2} $ of dimension one. We define Sidon arrays which are combinatorial objects giving a partition of the group $\mathbb {Z}_{q ^ 2} $ as a union of Sidon sets. We also use linear recurring sequences to quickly obtain Bose-type Sidon sets without the need to use the discrete logarithm.

Keywords

Sidon setslinear recurrencesfinite fields

MSC classification

Primary: 11B13: Additive bases, including sumsets
Secondary: 11T06: Polynomials
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 106 , Issue 3 , December 2022 , pp. 376 - 384
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Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.

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