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Title of Journal: Des Codes Cryptogr

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Abbravation: Designs, Codes and Cryptography

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Springer US

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1573-7586

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On explicit factors of cyclotomic polynomials over

Authors: Liping Wang Qiang Wang
Publish Date: 2011/06/25
Volume: 63, Issue: 1, Pages: 87-104
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Abstract

We study the explicit factorization of 2 n rth cyclotomic polynomials over finite field mathbbF q where q r are odd with r q = 1 We show that all irreducible factors of 2 n rth cyclotomic polynomials can be obtained easily from irreducible factors of cyclotomic polynomials of small orders In particular we obtain the explicit factorization of 2 n 5th cyclotomic polynomials over finite fields and construct several classes of irreducible polynomials of degree 2 n–2 with fewer than 5 terms

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Other Papers In This Journal:
  1. Composition of recursions and nonlinear complexity of periodic binary sequences
  2. Practical-time attacks against reduced variants of MISTY1
  3. On the largest affine sub-families of a family of NFSR sequences
  4. The dimension of subcode-subfields of shortened generalized Reed–Solomon codes
  5. Two classes of optimal two-dimensional OOCs
  6. Sequences with small correlation
  7. Improved algorithms for finding low-weight polynomial multiples in $$\mathbb {F}_{2}^{}[x]$$ and some cryptographic applications
  8. A tight asymptotic bound on the size of constant-weight conflict-avoiding codes
  9. Distinguisher-based attacks on public-key cryptosystems using Reed–Solomon codes
  10. A new table of permutation codes
  11. Bent functions embedded into the recursive framework of $${\mathbb{Z}}$$ -bent functions
  12. Nonexistence of CW (110, 100)
  13. Point compression for the trace zero subgroup over a small degree extension field
  14. The Diffie–Hellman problem and generalization of Verheul’s theorem
  15. Modular independence and generator matrices for codes over $${\mathbb {Z}_m}$$
  16. Improved lower bounds on sizes of single-error correcting codes
  17. A combinatorial problem related to sparse systems of equations
  18. Some results concerning cryptographically significant mappings over GF(2 n )
  19. A note on the reducibility of binary affine polynomials
  20. Primitive normal bases for quartic and cubic extensions: a geometric approach
  21. Computing isogenies between supersingular elliptic curves over $${\mathbb {F}}_p$$
  22. Some cyclic codes of length 2 p n
  23. On the correlation distribution of Delsarte–Goethals sequences
  24. Algebraic decoding of folded Gabidulin codes
  25. Inner balance of symmetric designs
  26. On the construction of Griesmer codes of dimension 5
  27. Applications of representation theory to wireless communications
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