Hadamard-Walsh spectral characterization of Reed-Muller expansions

Computers and Electrical Engineering

Volumn 25, Issue 2, 1999, Pages 111-134

  Falkowski, Bogdan J ^a   Chang, Chip Hong ^b  

^a NANYANG TECHNOLOGICAL UNIVERSITY   (Singapore)

^b SCHOOL OF ENGINEERING   (Singapore)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; BOOLEAN FUNCTIONS; WALSH TRANSFORMS;

REED-MULLER EXPANSIONS;

INFORMATION THEORY;

EID: 0033098921     PISSN: 00457906     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0045-7906(98)00033-0     Document Type: Article

References (28)

1. Agrawal M., Arvind V. Polynomial time truth-table reductions to P-selective sets. Proc. 9th IEEE Annual Structure in Complexity Theory Conference, Amsterdam (June-July 1994), pp. 24-30.
2. Blahut R.E. Theory and Practice of Error Control Codes. Reading: Addison-Wesley, 1983.
3. Chang C.H., Falkowski B.J., Flexible optimization of fixed polarity Reed-Muller expansions for multiple output completely and incompletely specified Boolean functions. Proc. IEEE/IEICE Asia and South Pacific Design Automation Conf., August 1995 (ASP-DAC '95). Makuhari, Chiba, pp. 335-340.
4. Damarla TR, Karpovsky M. Fault detection in combinational networks by Reed-Muller transforms. IEEE Trans. Comput. 1989;38(6):788-97.
5. Davio P., Deschamps J.P., Thayse A. Discrete and Switching Functions. New York: George and McGraw-Hill, 1978.
6. t and Reed-Muller codes. IEEE Trans. Information Theory 1991;37(3):664-7.
7. Falkowski B.J., Chang C.H. Generation of fixed polarity Reed-Muller expansions from subset of Walsh spectral coefficients for completely specified Boolean functions. Proc. 5th Int. Workshop on Spectral Techniques (IWST), March 1994, Beijing, pp. 214-219.
8. Falkowski BJ, Chang CH. An exact minimizer of fixed polarity Reed-Muller expansions. Int. J. Electronics 1995;79(4):389-409.
9. Falkowski BJ, Schaefer I, Perkowski MA. Effective computer methods for the calculation of Rademacher-Walsh spectrum for completely and incompletely specified Boolean functions. IEEE Trans. on Computer-Aided Design 1992;11(10):1207-26.
10. Fujisawa T., Kasami T. Mathematics for Electronics and Communications Engineers, Theory of Discrete Structure. Tokyo: Korona, 1977 (in Japanese).
11. Harking B. Efficient algorithm for canonical Reed-Muller expansions of Boolean functions. IEE Proc. Part E 1990;137(5):366-70.
12. Harrison M. Introduction to Switching and Automata Theory. New York: McGraw-Hill, 1965.
13. Hirose S, Ikeda K. Relationships among nonlinearity criteria of Boolean functions. IEICE Trans. Fundamentals 1995;E78-A(2):235-42.
14. Hirose S, Ikeda K. Complexity of Boolean functions satisfying the propagation criterion. IEICE Trans. Fundamentals 1995;E78-A(4):470-7.
15. Hurst S.L., Miller D.M., Muzio J.C. Spectral Techniques in Digital Logic. London: Academic Press, 1985.
16. Kranakis E. Primality and Cryptography. Stuttgart: John Wiley & B.G. Teubner, 1987.
17. Karpovsky M.G. Finite Orthogonal Series in Design of Digital Devices. New York: Wiley, 1976.
18. MacWilliams F.J., Sloane N.J.A. The Theory of Error-Correcting Codes. Amsterdam: Elsevier Science Publishers, North-Holland, 1977.
19. Peile RE. The analysis of partial truth tables. IEEE Trans. Information Theory 1991;37(5):1479-86.
20. Pellerin D., Holley M. Practical Design Using Programmable Logic. Englewood Cliffs: Prentice-Hall, 1991.
21. Reddy SM. Easily testable realizations for logic functions. IEEE Trans. Comput. 1972;21(11):1183-8.
22. Reddy BRK, Pai AL. Reed-Muller transform image coding. Comput. Vision Graph. Image Proc. 1988;42(1):48-61.
23. Rhee M.Y. Error-Correcting Coding Theory. New York: McGraw-Hill, 1989.
24. Sasao T. (Ed.). Logic Synthesis and Optimization. Boston: Kluwer Academic, 1993.
25. Siu K.Y., Roychowdhury V., Kailath T. Discrete Neural Computation, A Theoretical Foundation. Englewood Cliffs: Prentice Hall, 1995.
26. Stankovic RS. A note of the relation between Reed-Muller expansions and Walsh transforms. IEEE Trans. Electromagn. Compat. 1982;24(1):68-70.
27. Xiao GZ, Massey JL. A spectral characterization of correlation-immune combining functions. IEEE Trans. Information Theory 1988;34(3):569-71.
28. Zhang YZ, Rayner PJW. Minimisation of Reed-Muller polynomials with fixed polarity. IEE Proc. Part E 1984;131(5):177-86