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The trace spectra of polynomial bases for \({\mathbb{F}}_{2^{n}}\)

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Abstract

In this paper we study the trace spectra of polynomial bases for \({\mathbb{F}}_{2^{n}}\) over \({\mathbb{F}}_{2}\) . Shparlinski showed that there exists a polynomial basis having O(log n) elements of trace one. Here we show that for every t ≤ n, there exists a polynomial basis having t + O(log n) elements of trace one. We also study consequences of our results to the existence of irreducible polynomials of certain weights.

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  1. Department of Combinatorics and Optimization, University of Waterloo, Waterloo, ON, N2L 3G1, Canada

    Omran Ahmadi

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  1. Omran Ahmadi
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Correspondence to Omran Ahmadi.

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Ahmadi, O. The trace spectra of polynomial bases for \({\mathbb{F}}_{2^{n}}\) . AAECC 18, 391–396 (2007). https://doi.org/10.1007/s00200-007-0044-y

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  • DOI: https://doi.org/10.1007/s00200-007-0044-y

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