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Using rational idempotents to show Turyn’s bound is sharp

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Abstract

Davis, Dillon, and Jedwab all showed the existence of difference sets in groups \({C_{2^{r+2}}\times C_{2^{r}}}\) . Turyn’s bound had previously shown that abelian 2-groups with higher exponents could not admit difference sets. We give a new construction technique that utilizes character values, rational idempotents, and tiling structures to produce Hadamard difference sets in the group \({C_{2^{r+2}}\times C_{2^{r}}}\) to replicate the result.

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Authors and Affiliations

  1. Department of Mathematics, Mid Michigan Community College, Mount Pleasant, MI, USA

    Jordan D. Webster

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  1. Jordan D. Webster
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Correspondence to Jordan D. Webster.

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Communicated by Q. Xiang.

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Webster, J.D. Using rational idempotents to show Turyn’s bound is sharp. Des. Codes Cryptogr. 62, 357–365 (2012). https://doi.org/10.1007/s10623-011-9526-9

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  • DOI: https://doi.org/10.1007/s10623-011-9526-9

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