Parameter Determination for Complex Number-Theoretic Transforms Using Cyclotomic Polynomials
- 1 January 1989
- journal article
- Published by JSTOR in Mathematics of Computation
- Vol. 52 (185) , 189-200
- https://doi.org/10.2307/2008663
Abstract
Some new results for finding all convenient moduli m for a complex number-theoretic transform with given transform length n and given primitive nth root of unity modulo m are presented. The main result is based on the prime factorization for values of cyclotomic polynomials in the ring of Gaussian integers.Keywords
This publication has 6 references indexed in Scilit:
- Factorizations of 𝑏ⁿ±1, 𝑏=2, 3, 5, 6, 7, 10, 11, 12 Up to High PowersContemporary Mathematics, 1988
- Prime factorizations for values of cyclotomic polynomials in ?[i]Archiv der Mathematik, 1987
- Number-Theoretic Transforms of Prescribed LengthMathematics of Computation, 1986
- The generalized discrete Fourier transform in rings of algebraic integersIEEE Transactions on Acoustics, Speech, and Signal Processing, 1980
- A new algorithm for computing primitive elements in the field of Gaussian complex integers modulo a Mersenne primeIEEE Transactions on Acoustics, Speech, and Signal Processing, 1979
- Introduction to Number Theory. By T. Nagell. Second Edition. Pp. 309. $5.50. 1964. (Chelsea.)The Mathematical Gazette, 1966