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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

10.1007/978-3-540-77600-0_11

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1573-7586

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Sequences with small correlation

Authors: KaiUwe Schmidt
Publish Date: 2015/11/30
Volume: 78, Issue: 1, Pages: 237-267
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Abstract

The extent to which a sequence of finite length differs from a shifted version of itself is measured by its aperiodic autocorrelations Of particular interest are sequences whose entries are 1 or 1 called binary sequences and sequences whose entries are complex numbers of unit magnitude called unimodular sequences Since the 1950s there is sustained interest in sequences with small aperiodic autocorrelations relative to the sequence length One of the main motivations is that a sequence with small aperiodic autocorrelations is intrinsically suited for the separation of signals from noise and therefore has natural applications in digital communications This survey reviews the state of knowledge concerning the two central problems in this area How small can the aperiodic autocorrelations of a binary or a unimodular sequence collectively be and how can we efficiently find the best such sequences Since the analysis and construction of sequences with small aperiodic autocorrelations is closely tied to the often much easier analysis of periodic autocorrelation properties several fundamental results on corresponding problems in the periodic setting are also reviewed

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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. 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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