511,761 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 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
Linear programming bounds for doubly-even self-dual codes
Using a variant of linear programming method 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 d/n <=166315 + o(1), thus improving on the Mallowsâ
OdlyzkoâSloane bound of 1/6. To establish this, we prove that in any doubly even-self-dual code the distance distribution is asymptotically upper-bounded by the corresponding normalized binomial distribution in a certain interval
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