Families of sequences with good family complexity and cross-correlation measure
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| Format: | Preprint |
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2020
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| _version_ | 1866913342855053312 |
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| author | Doğan, Kenan Şahin, Murat Yayla, Oğuz |
| author_facet | Doğan, Kenan Şahin, Murat Yayla, Oğuz |
| contents | In this paper we study pseudorandomness of a family of sequences in terms of two measures, the family complexity ($f$-complexity) and the cross-correlation measure of order $\ell$. We consider sequences not only on binary alphabet but also on $k$-symbols ($k$-ary) alphabet. We first generalize some known methods on construction of the family of binary pseudorandom sequences. We prove a bound on the $f$-complexity of a large family of binary sequences of Legendre-symbols of certain irreducible polynomials. We show that this family as well as its dual family have both a large family complexity and a small cross-correlation measure up to a rather large order. Next, we present another family of binary sequences having high $f$-complexity and low cross-correlation measure. Then we extend the results to the family of sequences on $k$-symbols alphabet. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2004_13938 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Families of sequences with good family complexity and cross-correlation measure Doğan, Kenan Şahin, Murat Yayla, Oğuz Information Theory Cryptography and Security Number Theory 11K45, 94A55, 94A60 In this paper we study pseudorandomness of a family of sequences in terms of two measures, the family complexity ($f$-complexity) and the cross-correlation measure of order $\ell$. We consider sequences not only on binary alphabet but also on $k$-symbols ($k$-ary) alphabet. We first generalize some known methods on construction of the family of binary pseudorandom sequences. We prove a bound on the $f$-complexity of a large family of binary sequences of Legendre-symbols of certain irreducible polynomials. We show that this family as well as its dual family have both a large family complexity and a small cross-correlation measure up to a rather large order. Next, we present another family of binary sequences having high $f$-complexity and low cross-correlation measure. Then we extend the results to the family of sequences on $k$-symbols alphabet. |
| title | Families of sequences with good family complexity and cross-correlation measure |
| topic | Information Theory Cryptography and Security Number Theory 11K45, 94A55, 94A60 |
| url | https://arxiv.org/abs/2004.13938 |