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Algebraic complexities and algebraic curves over finite fields
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We consider the problem of minimal (multiplicative) complexity of polynomial multiplication and multiplication in finite extensions of fields. For infinite fields minimal complexities are known [Winograd, S. (1977)
Math. Syst. Theory
10, 169-180]. We prove lower and upper bounds on minimal complexities over finite fields, both linear in the number of inputs, using the relationship with linear coding theory and algebraic curves over finite fields.
Proceedings of the National Academy of Sciences
Title: Algebraic complexities and algebraic curves over finite fields
Description:
We consider the problem of minimal (multiplicative) complexity of polynomial multiplication and multiplication in finite extensions of fields.
For infinite fields minimal complexities are known [Winograd, S.
(1977)
Math.
Syst.
Theory
10, 169-180].
We prove lower and upper bounds on minimal complexities over finite fields, both linear in the number of inputs, using the relationship with linear coding theory and algebraic curves over finite fields.
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