Abstract
We introduce t-density for codes to find either the exact value of or an upper bound on the covering radius of even subcodes. We find results on the number of cosets of maximum weight of even subcodes. Exact results are obtained for, among others, the s-error-correcting BCH codes (s=1,2,3), punctured RM codes, and some QR codes. An algorithm for computing covering radius of t-deficient codes is used in one case. Some extensions are announced.
Preliminary versions of this paper were presented at the IEEE International Symposium on Information Theory, Brighton, June 24–28, 1985, and at AAECC, the 3rd International Conference on Applied Algebra, Algebraic Algorithms, and Error-correcting Codes, Grenoble, July 15–19, 1985.
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E.F. Assmus, Jr. and Vera Pless, “On the covering radius of extremal self-dual codes,” IEEE Trans. Inform. Theory, vol. IT-29, pp. 359–363, 1983.
Gérard D. Cohen, Mark R. Karpovsky, H.F. Mattson, Jr., and James R. Schats, “Covering Radius-Survey and Recent Results,” IEEE Trans. Inform. Theory, vol. IT-31, pp. 328–343, 1985.
J. H. Conway and V. Pless, “On the enumeration of self dual codes,” J. Comb. Theory, vol. 28, pp. 26–53, 1980.
Ph. Delsarte, “Four fundamental parameters of a code and their combinatorial significance,” Inform. and Control, vol. 23, pp. 407–438, 1973.
Diane E. Downey and N. J. A. Sloane, “The covering radius of cyclic codes of length up to 31,” Trans. Inform. Theory, vol. IT-31, pp. 446–447, 1985.
D. Gorenstein, W. W. Peterson, and N. Zierler, “Two-error correcting Bose-Chaudhuri codes are quasi-perfect,” Inform. Contr., vol. 3, pp. 291–294, 1960.
R. L. Graham and N. J. A. Sloane, “On the covering radius of codes,” IEEE Trans. Inform. Theory, vol. IT-31, pp. 385–401, 1985.
T. Helleseth, “All binary 3-error correcting BCH codes of length 2m — 1 have covering radius 5,” IEEE Trans. Inform. Theory, vol. IT-24, pp. 257–258, 1978.
T. Helleseth, T. Kløve, and J. Mykkeltveit, “On the covering radius of binary codes,” IEEE Trans. Inform. Theory, vol. IT-24, pp. 627–628, 1978.
F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, North Holland, Amsterdam, 1977.
A. McLoughlin, “The covering radius of the (m−3)rd order Reed-Muller codes and a lower bound on the (m−4)th order Reed-Muller codes,” SIAM J. Appl. Math. vol. 37, pp. 419–422, 1979.
W. W. Peterson and E. J. Weldon, Jr., Error-Correcting Codes, 2nd ed., (MIT Press, 1972).
G. Seroussi and A. Lempel, “Maximum likelihood decoding of certain Reed-Muller codes,” IEEE Trans Inform. Theory, vol. IT-29, No. 3, May 1983.
G. D. Cohen, A. C. Lobstein, and N. J. A. Sloane, “Further results on the covering radius of codes,” to appear.
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© 1986 Springer-Verlag Berlin Heidelberg
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Janwa, H., Mattson, H.F. (1986). Covering radii of even subcodes of t-dense codes. In: Calmet, J. (eds) Algebraic Algorithms and Error-Correcting Codes. AAECC 1985. Lecture Notes in Computer Science, vol 229. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-16776-5_714
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DOI: https://doi.org/10.1007/3-540-16776-5_714
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