Upper bound on list-decoding radius of binary codes

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Consider the problem of packing Hamming balls of a given relative radius subject to the constraint that they cover any point of the ambient Hamming space with multiplicity at most L. For odd L≥ 3 an asymptotic upper bound on the rate of any such packing is proven. Resulting bound improves the best known bound (due to Blinovsky'1986) for rates below a certain threshold. Method is a superposition of the linear-programming idea of Ashikhmin, Barg and Litsyn (that was used previously to improve the estimates of Blinovsky for L=2) and a Ramsey-theoretic technique of Blinovsky. As an application it is shown that for all odd L the slope of the rate-radius tradeoff is zero at zero rate.