Constructions for Perfect Maps and Pseudorandom Arrays

IEEE Transactions on Information Theory

Volumn 34, Issue 5, 1988, Pages 1308-1316

  Etzion, Tuvi ^a  

^a UNIVERSITY OF SOUTHERN CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTERS, DIGITAL--SHIFT REGISTERS; MATHEMATICAL TECHNIQUES--MATRIX ALGEBRA;

BINARY ARRAYS; PERFECT MAPS; PSEUDORANDOM ARRAYS; PSEUDORANDOM SEQUENCES; SHIFT REGISTER SEQUENCES;

COMPUTER METATHEORY;

EID: 0024079392     PISSN: 00189448     EISSN: 15579654     Source Type: Journal    
DOI: 10.1109/18.21260     Document Type: Article

References (23)

1. I. S. Reed and R. M. Stewart, “Note on the existence of perfect maps,” IRE Trans. Inform. Theory, vol. IT-8, pp. 10–12, Jan. 1962.
2. S. L. Ma, “A note on binary arrays with a certain window property,” IEEE Trans. Inform. Theory, vol. IT-30, pp. 774–775, Sept. 1984.
3. C. T. Fan, S. M. Fan, S. L. Ma, and M. K. Siu, “On de Bruijn arrays,” Ars Combinatoria, vol. 19A, pp. 205–213, May 1985.
4. B. Gordon, “On the existence of perfect maps,” IEEE Trans. Inform. Theory, vol. IT-12, pp. 486–487, Oct. 1966.
5. F. J. MacWilliams and N. J. A. Sloane, “Pseudo-random sequences and arrays,” Proc. IEEE, vol. 64, pp. 1715–1729, Dec. 1976.
6. T. Nomura, H. Miyakawa, H. Imai, and A. Fukuda, “A theory of two-dimensional linear recurring arrays,” IEEE Trans. Inform. Theory, vol. IT-18, pp. 775–785, Nov. 1972.
7. J. H. van Lint, F. J. MacWilliams, and N. J. A. Sloane, “On pseudo-random arrays,” SIAM J. Appl. Math., vol. 36, pp. 62–72, Feb. 1979.
8. N. G. de Bruijn, “A combinatorial problem,” Nederl. Akad. Wetensch. Proc., vol. 49, pp. 758–764, 1946.
9. S. W. Golomb, Shift Register Sequences. Laguna Hills, CA: Aegean Park Press, 1982.
10. H. M. Fredricksen, “A survey of full length nonlinear shift register cycle algorithms,” SIAM Rev., vol. 24, pp. 195–221, Apr. 1982.
11. T. van Aardenne-Ehrenfest and N. G. de Bruijn, “Circuits and trees in ordered linear graphs,” Simon Steven, vol. 28, pp. 203–217, 1951.
12. H. M. Fredricksen and J. Maiorana, “Necklaces of beads in k colors and k-ary de Bruijn sequences,” Discrete Math., vol. 23, pp. 207–210, Sept. 1978.
13. A. Ralston, “A new memoryless algorithm for de Bruijn sequences,” J. Algorithms, vol. 2, pp. 50–62, Mar. 1981.
14. T. Etzion, “An algorithm for constructing m-ary de Bruijn sequences,” J. Algorithmsvol. 7, pp. 331–340, Sept. 1986.
15. H. Fredricksen, “A class of non-linear de Bruijn cycles,” J. Cornbin. Theory, Ser. A, vol. 19, pp. 191–199, Sept. 1975.
16. T. Etzion and A. Lempel, “Algorithms for the generation of full-length shift-register sequences,” IEEE Trans. Inform. Theory, vol. IT-30, pp. 480–484, May 1984.
17. A. H. Chan, R. A. Games, and E. L. Key, “On the complexities of de Bruijn sequences,” J. Combin. Theory, Ser. A, vol. 33, pp. 233–246, Nov. 1982.
18. A. Lempel, “On a homomorphism of the de Bruijn graph and its applications to the design of feedback shift registers,” IEEE Trans. Comput., vol. C-19, pp. 1204–1209, Dec. 1970.
19. T. Etzion and A. Lempel, “Construction of de Bruijn sequences of minimal complexity,” IEEE Trans. Inform. Theory, vol. IT-30, pp. 705–709, Sept. 1984.
20. B. Elspas, “Theory of autonomous linear sequential networks,” IRE Trans. Circuit Theory, vol. CT-6, pp. 45–60, Mar. 1959.
21. R. W. Marsh, “Tables of irreducible polynomials over GF(2) through degree 19,” United States Dept. of Commerce, Washington, DC, 1957.
22. J. D. Alanen and D. E. Knuth, “Tables of finite fields,” Sankhya, Ser. A, vol. 26, pp. 305–328, Dec. 1964.
23. S. Mossige, “Tables of irreducible polynomials over GF[2] of degree 10 through 20,” Math. Comput., vol. 26, pp. 1007–1009, Oct. 1972.