Spectral orbits and peak-to-average power ratio of boolean functions with respect to the {I, H, N}n transform

Lecture Notes in Computer Science

Volumn 3486, Issue , 2005, Pages 373-388

  Danielsen, Lars Eirik ^a   Parker, Matthew G ^a  

^a UNIVERSITY OF BERGEN   (Norway)

Author keywords

[No Author keywords available]

Indexed keywords

ALGEBRA; GRAPH THEORY; INTEGRAL EQUATIONS; MATHEMATICAL TRANSFORMATIONS; QUADRATIC PROGRAMMING; QUANTUM THEORY;

CONSTRUCTION TECHNIQUE; PEAK-TO-AVERAGE POWER RATIO; SELF-DUAL ADDITIVE CODES; SPECTRAL ORBITS;

BOOLEAN FUNCTIONS;

EID: 24944509529     PISSN: 03029743     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1007/11423461_28     Document Type: Conference Paper

References (28)

1. Calderbank, A.R., Rains, E.M., Shor, P.M., Sloane, N.J.A.: Quantum error correction via codes over GF(4). IEEE Trans. Inform. Theory 44 (1998) pp. 1369-1387 http://arxiv.org/quant-ph/9608006.
2. Rains, E.M., Sloane, N.J.A.: Self-dual codes. In Pless, V.S., Huffman, W.C., eds.: Handbook of Coding Theory. Elsevier (1998) 177-294 http://arxiv.org/math/0208001.
3. Höhn, G.: Self-dual codes over the Kleinian four group. Mathematische Annalen 327 (2003) pp. 227-255 http://arxiv.org/math/0005266.
4. Hein, M., Eisert, J., Briegel, H.J.: Multi-party entanglement in graph states. Phys. Rev. A 69 (2004) http://arxiv.org/quant-ph/0307130.
5. Glynn, D.G., Gulliver, T.A., Maks, J.G., Gupta, M.K.: The geometry of additive quantum codes. Submitted to Springer-Verlag (2004)
6. Sloane, N.J.A.: The On-Line Encyclopedia of Integer Sequences. Web page (2004) http://www.research.att.com/~njas/sequences/.
7. Danielsen, L.E.: Database of self-dual quantum codes. Web page (2004) http://www.ii.uib.no/~larsed/vncorbits/.
8. Schlingemann, D., Werner, R.F.: Quantum error-correcting codes associated with graphs. Phys. Rev. A 65 (2002) http://arxiv.org/quant-ph/0012111.
9. Grassl, M., Klappenecker, A., Rotteler, M.: Graphs, quadratic forms, and quantum codes. In: Proc. IEEE Int. Symp. Inform. Theory. (2002) p. 45
10. Glynn, D.G.: On self-dual quantum codes and graphs. Submitted to Elect. J. Combinatorics. http://homepage.mac.com/dglynn/.cv/dglynn/Public/ SD-G3.pdf-link.pdf (2002)
11. Van den Nest, M., Dehaene, J., De Moor, B.: Graphical description of the action of local Clifford transformations on graph states. Phys. Rev. A 69 (2004) http://arxiv.org/quant-ph/0308151.
12. Parker, M.G., Rijmen, V.: The quantum entanglement of binary and bipolar sequences. In Helleseth, T., Kumar, P.V., Yang, K., eds.: Sequences and Their Applications, SETA'01. Discrete Mathematics and Theoretical Computer Science Series, Springer-Verlag (2001) Long version: http://arxiv.org/quant-ph/0107106.
13. Bouchet, A.: Isotropic systems. European J. Combin. 8 (1987) pp. 231-244
14. Bouchet, A.: Recognizing locally equivalent graphs. Discrete Math. 114 (1993) pp. 75-86
15. McKay, B.D.: nauty User's Guide. (2004) http://cs.anu.edu.au/~bdm/nauty/ nug.pdf.
16. Gulliver, T.A., Kim, J.-L.: Circulant based extremal additive self-dual codes over GF(4). IEEE Trans. Inform. Theory 50 (2004) pp. 359-366
17. min for additive [[n, k, d}} QECC. Web page (2003) http://iaks-www.ira.uka.de/home/grassl/QECC/TableIII.html.
18. Riera, C., Petrides, G., Parker, M.G.: Generalized bent criteria for Boolean functions. Technical Report 285, Dept. of Informatics, University of Bergen, Norway (2004) http://www.ii.uib.no/publikasjoner/texrap/pdf/2004-285. pdf.
19. Parker, M.G.: Generalised S-box nonlinearity. NESSIE Public Document, NES/DOC/UIB/WP5/020/A. https://www.cosic.esat.kuleuven.ac.be/ nessie/reports/phase2/SBoxLin.pdf (2003)
20. Danielsen, L.E., Gulliver, T.A., Parker, M.G.: Aperiodic propagation criteria for Boolean functions. Submitted to Inform. Comput. http://www.ii.uib.no/~matthew/GenDiff4.pdf (2004)
21. Radziszowski, S.P.: Small Ramsey numbers. Elect. J. Combinatorics (2002) pp. 1-42 Dynamical Survey DS1, http://www.combinatorics.org/Surveys/ds1.pdf.
22. Arratia, R., Bollobás, B., Sorkin, G.B.: The interlace polynomial of a graph. J. Combin. Theory Ser. B 92 (2004) pp. 199-233 http://arxiv.org/ math/0209045.
23. Aigner, M., van der Holst, H.: Interlace polynomials. Linear Algebra and its Applications 377 (2004) pp. 11-30
24. Riera, C., Parker, M.G.: Spectral interpretations of the interlace polynomial. Submitted to WCC2005. http://www.ii.uib.no/~matthew/WCC4.pdf (2004)
25. Parker, M.G., Gulliver, T.A.: On graph symmetries and equivalence of the six variable double-clique and wheel. Unpublished (2003)
26. Parker, M.G., Tellambura, C.: A construction for binary sequence sets with low peak-to-average power ratio. In: Proc. IEEE Int. Symp. Inform. Theory. (2002) p. 239 http://www.ii.uib.no/~matthew/634isit02.pdf.
27. Parker, M.G., Tellambura, C.: A construction for binary sequence sets with low peak-to-average power ratio. Technical Report 242, Dept. of Informatics, University of Bergen, Norway (2003) http://www.ii.uib.no/ publikasjoner/texrap/pdf/2003-242.pdf.
28. Davis, J.A., Jedwab, J.: Peak-to-mean power control in OFDM, Golay complementary sequences and Reed-Muller codes. IEEE Trans. Inform. Theory 45 (1999) pp. 2397-2417