Báo cáo toán học: "On optimal linear codes over F8" pptx

... 229–268. [5] R. Hill, Optimal linear codes, in: C. Mitchell, ed., Cryptography and Coding II (Oxford Univ. Press, Oxford, 1992) 75–104. [6] R. Hill, An extension theorem for linear codes, Des. Codes Cryptogr. ... Lizak, Extensions of linear codes, Proc. IEEE Int. Symposium on Inform. Theory (Whistler, Canada, 1995) 345. [8] R. Hill, D.Z. Newton, Optimal ternary linear codes,...

Ngày tải lên: 08/08/2014, 12:23

... +2)g k (n) − kg k (n − 1) (12) Thus, x k (n), y k (n), f k (n)andg k (n) satisfy the same second order linear recursion. The ini- tial conditions are (x k (1),y k (1),f k (1),g k (1)) = (1, 1, 2, 1) ... 1 and b(2) = 2 for k>1. Here k is assumed to be a positive integer. It is tempting to try a linear function in n for b(n). At the same time, it is necessary that b(n) is a positive inte...

Ngày tải lên: 07/08/2014, 06:20

... counted according to the total size of those bad cycles. Multiply both sides by (−t) k and sum over all positive integers k ≤ n, to get D n,a (−t) = n  k=1  n  b=i k  i=0  c(n − b, k − i)m a (i, ... with k cycles according to the number of their 1-cycles. Multiply both sides by (−t) k and sum over all positive integers k ≤ n, to get D n (−t) = n  k=1  k  i=0  n i  c(n −i, k − i)...

Ngày tải lên: 07/08/2014, 13:21

... set of Pareto -optimal and weak Pareto -optimal alternatives, J. Optim. Theory Appl. 40 (1983) 537–557. 17. N. D. Yen and T. D. Phuong, Connectedness and Stability of the Solution Sets in Linear Fractional ... of linear fractional vector optimization problems. 1. Introduction The problem of minimizing or maximizing several linear fractional objective functions on a polyhedral convex s...

Ngày tải lên: 06/08/2014, 05:20

... the codes C(q, n). The details are left to the reader. One may notice some similarities between the codes constructed above and the codes belonging to two other classes, that is the classes of codes ... Error-Correcting Codes, North Holland, 1977 [10] Schmidt,W., Equations over finite fields, an elementary approach, LNM, vol.536, Springer 1976 [11] Schoof, R., Families of curves and...

Ngày tải lên: 07/08/2014, 06:20

... “Table of Constant Weight Binary Codes, ” http://www.research.att.com/~njas /codes/ Andw/ [4] D. H. Smith, L. A. Hughes and S. Perkins, “A New Table of Constant Weight Codes of Length Greater than 28,” ... Bounds of A (n, d, w),” Designs, Codes and Cryptography 43:2/3 June 2007. the electronic journal of combinatorics 14 (2007), #N13 6 New Optimal Constant Weight Codes I. Gashkov ∗ ,...

Ngày tải lên: 07/08/2014, 13:21

... 303–323. [12] I. Honkala, A family of optimal identifying codes in ZZ 2 , J. Combin. Theory, Ser. A, 113 (2006), pp. 1760–1763. [13] I. Honkala, On 2-edge-robust r-identifying codes in the king grid, Australas. ... class of codes for identi- fying vertices in graphs, IEEE Trans. Inform. Theory 44 (1998), pp. 599–611. [19] T. Laihonen, On optimal edge-robust and vertex-robust (1, ≤ l...

Ngày tải lên: 07/08/2014, 15:22

... y is R-covered by C if d(y, C) ≤ R and that C  ⊂ Q n is R-covered by C, if every y ∈ C  is R-covered by C. A code C ⊂ Q n of length n has covering radius (at most) R, if Q n is R-covered by ... Lint, J.H.: On Codes with Covering Radius 1 and Minimum Distance 2, Indag. Math. (N.S.), 12 (2001), 449-452. [2] Cohen, G. / Honkala, I. / Litsyn, S. / Lobstein, A.: Covering Codes, North-Holland,...

Ngày tải lên: 07/08/2014, 15:22

... A. Brouwer, Tables of general binary codes, http://www.win.tue.nl/∼aeb /codes/ binary-1.html. [3] G. Cohen, I.S. Honkala, S. Litsyn, A. Lobstein, Covering codes, North Hol- land Mathematical Library, ... 1719-1731. [6] W. Haas, Lower bounds for q-ary codes of covering radius one, Discr. Mathematics 219 (2000), 97-106. [7] W. Haas, Binary and ternary codes with covering radius one: Some...

Ngày tải lên: 07/08/2014, 15:23

... integer. A linear equation or a system of linear equations L is r-regular if every r-coloring of positive integers admits a monochromatic solution to L. Hence Theorem 1 states that a linear homogeneous ... Moreover, a recent result by Alekseev and Tsimerman [1] affirmatively settled Rado’s conjecture that for any r  3 there is a homogeneous linear equation that is not r-regular. We say...

Ngày tải lên: 08/08/2014, 12:22