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On Unordered Codes
February 1991 (vol. 40 no. 2)
pp. 125-131

By extending the results obtained by D. E. Knuth (1986), a parallel unordered coding scheme with 2/sup r/ information bits is described. Balanced codes in which each codeword contains equal amounts of zeros and ones, with r check bits and up to 2/sup r+1/-(r+2) information bits, are constructed. Unordered codes with r check bits and up to 2/sup r/+2/sup r-1/-1 information bits are designed. Codes capable of detecting 2/sup r-1/+(2/sup r//2)-1 unidirectional errors using r check bits are also described. A review of previous work is presented.

[1] E. L. Leiss, "Data integrity in digital optical disks,"IEEE Trans. Comput., vol. C-33, no. 9, pp. 818-827, Sept. 1984.
[2] J. M. Berger, "A note on error detecting codes for asymmetric channels,"Inform. Contr., vol. 4, pp. 68-73, Mar. 1961.
[3] C.V. Freiman, "Optimal error detecting codes for completely asymmetric binary channels,"Inform. Contr., vol. 5, pp. 64-71, Mar. 1962.
[4] J. E. Smith, "On separable unordered codes,"IEEE Trans. Comput., vol. C-33, no. 8, pp. 741-743, Aug. 1984.
[5] J. M. Borden, "Optimal asymmetric error detecting codes,"Inform. Contr., vol. 53, no. 1/2, pp. 66-73, Apr./May 1982.
[6] B. Bose and D. J. Lin, "Systematic unidirectional error-detecting codes,"IEEE Trans. Comput., vol. C-34, no. 11, pp. 1026-1032, Nov. 1985.
[7] D. K. Pradhan and J. J. Stiffler, "Error correcting codes and self-checking circuits in fault-tolerant computers,"IEEE Comput. Mag., vol. 13, pp. 27-37, Mar. 1980.
[8] D.E. Knuth, "Efficient balanced codes,"IEEE Trans. Inform. Theory, vol. IT-32, no. 1, pp. 51-53, Jan. 1986.
[9] E. Sperner, "Ein Satzüber Untermengen einer endlichen Menge,"Math. Zeitschrift, vol. 27, no. 1, pp. 544-548, 1928.
[10] B. Bose and D. K. Pradhan, "Optimal unidirectional error detecting/correcting codes,"IEEE Trans. Comput., vol. C-31, no. 6, pp. 564-568, June 1982.
[11] T. M. Cover, "Enumerative source encoding,"IEEE Trans. Inform. Theory, vol. IT-19, no. 1, pp. 73-77, Jan. 1973.
[12] Y. Tohma, R. Sakai, and R. Ohyama, "Realization of fail-safe sequential machines by usingk-out-of-ncode,"IEEE Trans. Comput., vol. C-20, no. 11, pp. 1270-1275, Nov. 1971.
[13] Y. Takasakiet al, "Optical pulse formats for fiber optic digital communications,"IEEE Trans. Commun., vol. COM-24, pp. 404-413, 1976.
[14] A.X. Widmer and P.A. Franaszek, "A DC-balanced, partitioned-block, 8B/10B transmission code,"IBM J. Res. Develop., vol. 27, no. 5, pp. 440-451, Sept. 1983.
[15] N. K. Jha and M.B. Vora, "A systematic code for detectingt- unidirectional errors," inDig. Papers, 17th Int. Symp. Fault-Tolerant Comput., June 1987, pp. 96-101.

Index Terms:
unordered codes; parallel unordered coding scheme; zeros; ones; unidirectional errors; encoding; error correction codes.
Citation:
B. Bose, "On Unordered Codes," IEEE Transactions on Computers, vol. 40, no. 2, pp. 125-131, Feb. 1991, doi:10.1109/12.73583
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