Abstract:In this article, we present fast computational algorithms for Jacobi sums of orders l 2 and 2l 2 with odd prime l. Cyclotomic numbers play a crucial rule in implementing these algorithms. To increase efficiency, we present explicit expressions for Jacobi sums of orders l 2 and 2l 2 in terms of the minimum number of cyclotomic numbers of order l 2 and 2l 2 respectively, which will be utilized in implementing the algorithms. To validate these expressions, we implement two additional algorithms which demonstrate … Show more
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