New uniform and asymptotic upper bounds on the tensor rank of multiplication in extensions of finite fields
MATHEMATICS OF COMPUTATION(2015)
摘要
We obtain new uniform upper bounds for the tensor rank of the multiplication in the extensions of the finite fields F-q for any prime power q; moreover, these uniform bounds lead to new asymptotic bounds as well. In addition, we also give purely asymptotic bounds which are substantially better by using a family of Shimura curves defined over F-q, with an optimal ratio of F(q)t-rational places to their genus, where q(t) is a square.
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关键词
Algebraic function field,tower of function fields,tensor rank,algorithm,finite field
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