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Planar products of linearized polynomials

Abstract : Let L1(x) and L2(x) be linearized polynomials over Fqn. We determine conditions when the product L1(x) . L2(x) is a planar mapping on Fqn. For a linearized polynomial L over Fqn, let M(L) ={α∈Fqn : L(x) + α x is bijective on Fqn}. We show that the planarity of the product L1(x) . L2(x) is linked with the set M(L) of a suitable linearized polynomial L. We use this relation to describe some families of such planar mappings and we give some nonexistence results.
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Submitted on : Thursday, August 11, 2011 - 11:39:44 AM
Last modification on : Monday, May 30, 2022 - 5:36:02 PM
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Gohar Kyureghyan, Ferruh Özbudak. Planar products of linearized polynomials. WCC 2011 - Workshop on coding and cryptography, Apr 2011, Paris, France. pp.351-360. ⟨inria-00614431⟩

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