The gray code

Journal of Universal Computer Science

Volumn 13, Issue 11, 2007, Pages 1573-1597

  Doran, Robert W ^a  

^a UNIVERSITY OF AUCKLAND   (New Zealand)

Author keywords

Gray code; Single distance code

Indexed keywords

EID: 38749119363     PISSN: 0958695X     EISSN: 09486968     Source Type: Journal    
DOI: None     Document Type: Article

References (51)

1. Barr, K. G.: "A decimal Gray code"; Wireless World, Vol. 87, No. 1542, pp. 86-87, March 1981.
2. Beauchamp, K. G.: "Walsh functions and their applications"; Academic Press, 1975.
3. Bitner, J. R., Ehrlich, G., Reingold, E. M.: "Efficient generation of the binary reflected Gray code and its applications"; CACM, Vol. 19, No. 9, pp. 517-521, September. 76.
4. Boothroyd, J.: "Algorithm 246 Graycode"; CACM, Vol. 7, No. 12, p. 701, December 1964.
5. Burkhart, William H.: "Comment on "A Gray code counter""; IEEE Transactions on Computers, pp. 653-654, July 1970.
6. Cavior, S. R.: "Upper bounds associated with errors in Gray code"; IEEE Trans. Inf. Theory, Vol. IT-21, No. 5, p. 596, September 1975.
7. Chang, C. C., Chen, H. Y., Chen, C. Y.: "Symbolic Gray code as a data allocation scheme for two-disc systems"; Computer Journal, Vol. 35, No. 3, pp. 299-305, June 1992.
8. Chang, C. C., Lee, R. C. T., Du, M. W.: "Symbolic Gray code as a perfect multiattribute hashing scheme for partial match queries" ; IEEE Trans. Softw. Eng., SE-8, No. 3, pp. 235-249, 1982.
9. Cohn, M.: "Affine m-ary Gray codes"; Inform. Control. 6, pp. 70-78, 1963.
10. Cohn, M., Even, S.: "A Gray code counter"; IEEE Transactions on Computers, pp. 662-664, July 1969.
11. Darwood, N.: "Using the decimal Gray code"; Electronic Engineering (London), Vol. 44, No. 528, pp. 28-29, February 1972.
12. Deutsch, E. S.: "On the use of binary and Gray code schemes for continuoustone picture representation"; Pattern Recognition, Vol. 5, No. 2, pp. 121-132, June 1973.
13. Du, H. D., Lee, R. C. T.: "Symbolic Gray code as a multikey hashing function" ; IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. PAMI-2, No. 1, pp. 83-90, January 1980.
14. Er, M. C.: "On generating the n-ary reflected Gray codes"; IEEE Trans. Comput., Vol. C-33, No. 8, pp. 739-741, August, 1978.
15. Er, M. C.: "Remark on algorithm 246 (Gray code)"; ACM Trans Math Software. Vol. 11, No. 4, pp. 441-3, Dec 1985.
16. Foss, F. A.: "The use of a reflected code in digital control systems" ; IRE Trans. Elec. Comps, pp. 1-6, December 1954.
17. Fischmann, A. F.: "A Gray code counter"; IRE Trans Elec. Comp., Vol. EC-6, p. 120, June 1957.
18. Flajolet, P., Ramshaw, L.: "A note on Gray code and odd-even merge"; SIAM Journal on Computing, Vol. 9, No. 1, pp. 142-58, February 1980.
19. Ganesan, S.: "Fast 16 bit Gray code to binary code converter"; Electronic Engineering, p. 17, April 1980.
20. Gardner, M.: "The curious properties of the Gray code and how it can be used to solve puzzles"; Scientific American, 227, 2, pp. 106-109, August 1972.
21. Gilbert, E. N.: "Gray codes and paths on the n-cube"; Bell Syst Tech J., Vol. 37, pp. 815-826, May 1958.
22. Gray, F.: "Pulse Code Communication"; US patent #2,632,058. March 17th, 1953.
23. Heath, F. G.: "Origins of the Binary Code"; Scientific American, 227, 2, pp. 76-83, August 1972.
24. Irshid, M. I.: "Gray code weighting system"; IEEE Trans. Inform. Theory, Vol. 33, No. 6, pp. 930-931, 1987.
25. Kautz, W. H.: "A readily implemented single-error-correcting unit-distance counting code" ; IEEE Trans. Computers, Vol. C-19, pp. 972-975, 1970.
26. Kaye, R.: "A gray code for set partitions"; Information Processing Letters, Vol. 5, No. 6, pp. 171-173, 1976.
27. Klingsberg, P.: "A Gray code for compositions"; Journal of Algorithms, Vol. 3, No. 1, pp. 41-44, 1982.
28. Koda, Y., Ruskey, F.: "A Gray code for the ideals of a forest poset"; Journal of Algorithms, Vol. 15, No. 2, pp. 324-340, 1993.
29. Larcher, G., Tichy, R. F.: "A note on Gray code and odd-even merge"; Discrete Applied Mathematics, Vol. 18, No. 3, pp. 309-313, 1987.
30. Lippel, B.: "Comments on 'A fast analog to Gray code converter'"; Proceedings of the IEEE, Vol. 66, No. 7, pp. 797-798, July 1978.
31. Lucal, Harold M.: "Arithmetic operations for digital computers using a modified reflected binary code"; IEEE Transactions on Computers, pp. 449-458, December 1959.
32. Ludman, J. E.: "Gray code generation for MPSK signals"; IEEE Transactions on Communications, Vol. COM-29, No. 10, pp.1519-1522, October 1981.
33. Majithia, J C.: "Simple design for up/down Gray-code counters"; Electronics Letters, 4th November 1971, Vol. 7, No. 22, pp. 658-659.
34. Mecklenburg,P., Pehlert, W. K. Jr., Sullivan, D. D.: "Correction of errors in multilevel Gray-coded data"; IEEE Transactions on Information Theory, Vol. IT-19. No. 3, pp.336-340, May 1973.
35. Misra, J.: "Remark on algorithm 246: Graycode [Z]"; ACM Trans. Math. Software, Vol. 1, No. 3, p. 285, September 1975.
36. Proskurowski, A., Rusky, F.: "Binary tree Gray codes"; Journal of Algorithms, Vo.l 6, pp. 225-238, 1985.
37. Richards, D.: "Data, compression and Gray-code sorting"; Information Processing Letters, Vol. 22, No. 4, pp. 201-5, 17 April 1986.
38. Salzer, H. E.: "Ordering +or-f(+or-f(+or-f(...+or-f(x)...))) when f(x) is positive momotonic"; Communications of the ACM, Vol. 15, No. 1, p. 45, January 1972.
39. Salzer, H. E.: "Gray code and the +or-sign sequence when +or-f(+or-f(+or-f(...+or-f(x)...))) is ordered"; Communications of the ACM, Vol. 16, No. 3, p. 180, March 1973.
40. Savage, C. D.: "Gray code sequences of partitions"; Journal of Algorithms, Vol. 10, No. 4, pp. 577-95, December 1989.
41. Sharma, B. D., Khanna, R. K.: "On m-ary Gray codes"; Information Sciences, Vol. 15, pp. 31-43, 1978.
42. Thangavel, P., Muthuswamy, V. P.: "A parallel Algorithm to generate n-ary reflected Gray codes in a linear array with reconfigurable bus system"; Parallel Processing Letters, Vol. 3, No. 2, pp. 157-164, June 1993.
43. Takizawa, K., Okada, M.: "High-speed Gray-binary and binary-Gray code convertors using electro-optic light modulators" ; Electronics Letters, Vol. 14, No. 22, pp. 708-710, October 1978.
44. Walker, M.: "Decipher the Gray code"; Electron. Des., Vol. 18, No. 4 , pp. 70-74, February, 1970.
45. Wang, M. C.: "An algorithm for Gray to binary conversion"; IEEE Transactions on Electronic Computers, Vol. EC-5, No. 4, pp. 659-660, August 1966.
46. Worley, R. T., & Tischer, P. E.: "An alternative to Gray coding for bit-plane compression"; ACSC-17, Seventeenth Annual Computer Science Conference, Australian Computer Science Comunications, Vol. 16, No. 1, pp.189-197, January 1994.
47. Yuen, C.: "Walsh functions and Gray code"; IEEE Trans Electromagnetic Compatibility, Vol. EMC-13, pp. 68-73, August 1971.
48. Yuen, C. K.: "The separability of Gray code"; IEEE Transactions on Information Theory, Vol. IT-20, No. 5, pp. 668, September 1974.
49. Yuen, C. K.: "A fast analog to Gray code converter"; Proceedings of the IEEE Vol. 65, No. 10, pp. 1510-11, October 1977.
50. Yuen, C. K.: "Analog-to-Gray code conversion"; IEEE Transactions on Computers Vol. C-27, No. 10, pp. 971-973, October 1978.
51. Yuen, C. K.: "Binary division and square-rooting using gray code"; Technical report No. TRC8/88, Department of Information Systems and Computer Science, National University of Singapore, 1988. Seventeenth Annual ACM Computer Science Conference, p. 441, CA-DSP '89. 1989. International Symposium on Computer Architecture and Digital Signal Processing, Vol. 1, pp. 217-220, 1989.