Name
Abstract | ||
|---|---|---|
The spectral-null code S(n, k) of kth order and length n is the union of n-tuples with ±1 components, having kth-order spectral-null at zero frequency. We determine the exact asymptotic in n behavior of the size of such codes. In particular, we prove that for n satisfying some divisibility conditions, log2|S(n, k)|=n-k 2/2log2n+ck+o(1), where ck is a constant depending only on k and o(1) tends to zero when n grows. This is an improvement on the earlier known bounds due to Roth, Siegel, and Vardy (see ibid., vol40, p.1826-40, 1994) |
Year | DOI | Venue |
|---|---|---|
1999 | 10.1109/18.782100 | IEEE Transactions on Information Theory |
Keywords | Field | DocType |
kth-order spectral-null,kth order,high-order spectral-null code,spectral-null code,divisibility condition,asymptotically exact bound,length n,zero frequency,n behavior,known bound,exact asymptotic,polynomials,union,indexing terms,frequency,integral equations,lattices,codes,mathematics,exponential sum | Discrete mathematics,Combinatorics,Divisibility rule,Spectral analysis,Zero frequency,Mathematics | Journal |
Volume | Issue | ISSN |
45 | 6 | 0018-9448 |
Citations | PageRank | References |
4 | 0.95 | 9 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| G. Freiman | 1 | 4 | 0.95 |
| S. Litsyn | 2 | 602 | 50.31 |