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Multiplicative complexity of bilinear algorithms for cyclic convolution over finite fields

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Abstract

The multiplicative complexity of bilinear algorithms for cyclic convolution over finite fields is investigated. It is shown that mutually prime factor algorithms are inferior to directly designed algorithms for all lengths except those whose factors have relatively prime exponents. A previously described approach is proposed for directly designing algorithms which are highly structured and computationally efficient. Several complexity results are provided for factor lengths of specific form, and the manner in which cyclic convolution algorithms lead to linear algebraic error-correcting codes is discussed.

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Authors and Affiliations

  1. Department of Electrical Engineering, McGill University, Room 514—McConnell Engineering Building, 3480 University Street, H3A 2A7, Montreal, Quebec, Canada

    Salvatore D. Morgera

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  1. Salvatore D. Morgera
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Research supported by Natural Sciences and Engineering Research Council Canada Grant A0912.

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Morgera, S.D. Multiplicative complexity of bilinear algorithms for cyclic convolution over finite fields. Multidim Syst Sign Process 1, 99–111 (1990). https://doi.org/10.1007/BF01812210

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  • DOI: https://doi.org/10.1007/BF01812210

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