194 research outputs found
On the distance distribution of duals of BCH codes
We derive upper bounds on the components of the distance distribution of duals of BCH codes. Roughly speaking, these bounds show that the distance distribution can be upper-bounded by the corresponding normal distribution. To derive the bounds we use the linear programming approach along with some estimates on the magnitude of Krawtchouk polynomials of fixed degree in a vicinity of q/
On spectra of BCH codes
Derives an estimate for the error term in the binomial approximation of spectra of BCH codes. This estimate asymptotically improves on the bounds by Sidelnikov (1971), Kasami et al. (1985), and Sole (1990)
Estimates for the range of binomiality in codes' spectra
We derive new estimates for the range of binomiality in a codeâs spectra, where the distance distribution of a code is upperbounded by the corresponding normalized binomial distribution. The estimates
depend on the codeâs dual distance
On the accuracy of the binomial approximation to the distance distribution of codes
The binomial distribution is a well-known approximation to the distance spectra of many classes of codes. We derive a lower estimate for the deviation from the binomial approximatio
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An improved upper bound on the minimum distance of doubly-even self-dual codes
We derive a new upper bound on the minimum distance d of doubly-even self-dual codes of length n. Asymptotically, for n growing, it gives limnââ sup d/n <=(5-5^3/4)/10 <0.165630, thus improving on the Mallows-Odlyzko-Sloane bound of 1/6 and our recent bound of 0.16631
A note on the edge-reconstruction of K1,m-free graphs
AbstractWe show that there exists an absolute constant c such that any K1,m-free graph with the maximum degree Î > cm(log m)12 is edge reconstructible
Finding next-to-shortest paths in a graph
We study the problem of finding the next-to-shortest paths in a
graph. A next-to-shortest -path is a shortest -path
amongst -paths with length strictly greater than the length of
the shortest -path. In constrast to the situation in directed
graphs, where the problem has been shown to be NP-hard, providing edges of length zero are allowed,
we prove the somewhat surprising result that there is a polynomial
time algorithm for the undirected version of the problem
On a Reconstruction Problem for Sequences
AbstractIt is shown that any word of lengthnis uniquely determined by all its[formula]subwords of lengthk, providedkâ©Ÿâ167nâ+5. This improves the boundkâ©Ÿân/2â given in B. Manvelet al.(Discrete Math.94(1991), 209â219)
Switching reconstruction and diophantine equations
AbstractBased on a result of R. P. Stanley (J. Combin. Theory Ser. B 38, 1985, 132â138) we show that for each s â„ 4 there exists an integer Ns such that any graph with n > Ns vertices is reconstructible from the multiset of graphs obtained by switching of vertex subsets with s vertices, provided n â 0 (mod 4) if s is odd. We also establish an analog of P. J. Kelly's lemma (Pacific J. Math., 1957, 961â968) for the above s-switching reconstruction problem
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