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Linear programming bounds for doubly-even self-dual codes

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2 Author(s)
Krasikov, I. ; Sch. of Math. Sci., Tel Aviv Univ., Israel ; Litsyn, S.

Using a variant of the 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⩽0.166315···+o(1), thus improving on the Mallows-Odlyzko-Sloane 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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Information Theory, IEEE Transactions on  (Volume:43 ,  Issue: 4 )