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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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DOI

10.1016/0032-3950(77)90252-0

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1573-7586

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A note on the reducibility of binary affine polyno

Authors: Zhengjun Zhao Xiwang Cao
Publish Date: 2009/12/09
Volume: 57, Issue: 1, Pages: 83-90
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Abstract

Stickelberger–Swan Theorem is an important tool for determining parity of the number of irreducible factors of a given polynomial Based on this theorem we prove in this note that every affine polynomial Ax over mathbbF 2 with degree 1 where Ax = Lx + 1 and Lx=sum i=0nx2i is a linearized polynomial over mathbbF 2 is reducible except x 2 + x + 1 and x 4 + x + 1 We also give some explicit factors of some special affine pentanomials over mathbbF 2

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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. On explicit factors of cyclotomic polynomials over finite fields
  6. Two classes of optimal two-dimensional OOCs
  7. Sequences with small correlation
  8. Improved algorithms for finding low-weight polynomial multiples in $$\mathbb {F}_{2}^{}[x]$$ and some cryptographic applications
  9. A tight asymptotic bound on the size of constant-weight conflict-avoiding codes
  10. Distinguisher-based attacks on public-key cryptosystems using Reed–Solomon codes
  11. A new table of permutation codes
  12. Bent functions embedded into the recursive framework of $${\mathbb{Z}}$$ -bent functions
  13. Nonexistence of CW (110, 100)
  14. Point compression for the trace zero subgroup over a small degree extension field
  15. The Diffie–Hellman problem and generalization of Verheul’s theorem
  16. Modular independence and generator matrices for codes over $${\mathbb {Z}_m}$$
  17. Improved lower bounds on sizes of single-error correcting codes
  18. A combinatorial problem related to sparse systems of equations
  19. Some results concerning cryptographically significant mappings over GF(2 n )
  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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