Titlebook: Arithmetic of Finite Fields; 5th International Wo ?etin Kaya Ko?,Sihem Mesnager,Erkay Sava? Conference proceedings 2015 Springer Internatio

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https://doi.org/10.1007/978-1-4302-0133-5inite field . with very modest computational resources. Our . implementation was the first to illustrate the effectiveness of Joux’s algorithm for computing discrete logarithms in small-characteristic finite fields that are not Kummer or twisted-Kummer extensions.

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Dialog and Explanatory Components,lows us to prove the balance property of difference balanced functions from . to . where . is a prime power. We further prove two necessary and sufficient conditions for .-homogeneous difference balanced functions. This unifies several combinatorial objects related to difference balanced functions.

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Extending Graphically Specified Models, codes of length . over . quadratic residue codes over . are defined by their generating idempotents and their extension codes are discussed. Examples of codes and idempotents for small values of . and . are given. As a by-product almost MDS codes over . and . are constructed.

modish

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John K. Tsotsos,Tetsutaro Shibaharave or the function field sieve, requires solving large sparse systems of linear equations modulo the group order. Most of the fast algorithms used to solve such systems — e.g., the conjugate gradient or the Lanczos and Wiedemann algorithms — iterate a product of the corresponding sparse matrix with

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John K. Tsotsos,Tetsutaro Shibaharaelds. It is grounded on interpolation on algebraic curves: we give a theoretical lower threshold for the smallest bounds that one can expect from this method (with exceptions). This threshold appears often reachable: we moreover provide an explicit method for this purpose..We also provide new bounds

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