Name
Abstract | ||
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AbstractWe build on the work of Drakakis et al. (2011) on the maximal cross-correlation of the families of Welch and Golomb Costas permutations. In particular, we settle some of their conjectures. More precisely, we prove two results. First, for a prime $p\ge 5$ , the maximal cross-correlation of the family of the $\varphi (p-1)$ different Welch Costas permutations of $\{1,\ldots,p-1\}$ is $(p-1)/t$ , where $t$ is the smallest prime divisor of $(p-1)/2$ if $p$ is not a safe prime and at most $1+p^{1/2}$ otherwise. Here $\varphi $ denotes Euler’s totient function and a prime $p$ is a safe prime if $(p-1)/2$ is also prime. Second, for a prime power $q\ge 4$ the maximal cross-correlation of a subfamily of Golomb Costas permutations of $\{1,\ldots,q-2\}$ is $(q-1)/t-1$ if $t$ is the smallest prime divisor of $(q-1)/2$ if $q$ is odd and of $q-1$ if $q$ is even provided that $(q-1)/2$ and $q-1$ are not prime, and at most $1+q^{1/2}$ otherwise. Note that we consider a smaller family than Drakakis et al. Our family is of size $\varphi (q-1)$ whereas there are $\varphi (q-1)^{2}$ different Golomb Costas permutations. The maximal cross-correlation of the larger family given in the tables of Drakakis et al. is larger than our bound (for the smaller family) for some $q$ . |
Year | DOI | Venue |
|---|---|---|
2020 | 10.1109/TIT.2020.3009880 | Periodicals |
Keywords | DocType | Volume |
Costas arrays, permutations, cross-correlation, Welch construction, Golomb construction, radar, sonar | Journal | 66 |
Issue | ISSN | Citations |
12 | 0018-9448 | 0 |
PageRank | References | Authors |
0.34 | 0 | 2 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Domingo Gomez-perez | 1 | 61 | 10.22 |
| A. Winterhof | 2 | 49 | 5.80 |