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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

10.1002/9780470186510.ch3

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1573-7586

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Inner balance of symmetric designs

Authors: Tomas Nilson Pia Heidtmann
Publish Date: 2012/07/22
Volume: 71, Issue: 2, Pages: 247-260
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Abstract

A triple array is a rowcolumn design which carries two balanced incomplete block designs BIBDs as substructures McSorley et al Des Codes Cryptogr 35 21–45 2005 Section 8 gave one example of a triple array that also carries a third BIBD formed by its rowcolumn intersections This triple array was said to be balanced for intersection and they made a search for more such triple arrays among all potential parameter sets up to some limit No more examples were found but some candidates with suitable parameters were suggested We define the notion of an inner design with respect to a block for a symmetric BIBD and present criteria for when this inner design can be balanced As triple arrays in the canonical case correspond to SBIBDs this in turn yields new existence criteria for triple arrays balanced for intersection In particular we prove that the residual design of the related SBIBD with respect to the defining block must be quasisymmetric and give necessary and sufficient conditions on the intersection numbers This together with our parameter bounds enable us to exclude the suggested triple array candidates in McSorley et al Des Codes Cryptogr 35 21–45 2005 and many others in a wide search Further we investigate the existence of SBIBDs whose inner designs are balanced with respect to every block We show as a key result that such SBIBDs must possess the quasi3 property and we answer the existence question for all known classes of these designs


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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. A note on the reducibility of binary affine polynomials
  21. Primitive normal bases for quartic and cubic extensions: a geometric approach
  22. Computing isogenies between supersingular elliptic curves over $${\mathbb {F}}_p$$
  23. Some cyclic codes of length 2 p n
  24. On the correlation distribution of Delsarte–Goethals sequences
  25. Algebraic decoding of folded Gabidulin codes
  26. On the construction of Griesmer codes of dimension 5
  27. Applications of representation theory to wireless communications

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