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For r-~2 let p(n, r) denote the maximum cardinality of a subset A of N={1, 2 .... , n} such that there are no Bc A and an integer y with S b=y'. It is shown that for any e >-0 and bEB n>-n(e), (l+o(l))2~/t'+l>n('-l>/t'+l)~_p(n, r)~_n~ § for all r_~5, and that for every fixed r~_6, p(n,r)=(l+o(1)).21/t'+~)n (~-1)/(' § as n~. Let f(n,m) denote… (More)

The spectral-null code S(n; k) of k-th order and length n is the union of n-tuples with 1 components, having k-th order spectral null at zero frequency. We determine the exact asymptotic in n behaviour of the size of such codes. In particular, we prove that for n satisfying some divisibility conditions, log 2 jS(n; k)j = n ? k 2 2 log 2 n + c k + o(1),… (More)

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