TY - JOUR

T1 - Measures of pseudorandomness for finite sequences

T2 - Minimal values

AU - Alon, N.

AU - Kohayakawa, Y.

AU - Mauduit, C.

AU - Moreira, C. G.

AU - Rödl, V.

PY - 2006/1

Y1 - 2006/1

N2 - Mauduit and Sárközy introduced and studied certain numerical parameters associated to finite binary sequences EN ∈ {-1,1}N in order to measure their 'level of randomness'. Two of these parameters are the normality measure N(EN)$ and the correlation measure $C_k(E_N)$ of order k, which focus on different combinatorial aspects of $E_N$. In their work, amongst others, Mauduit and Sárközy investigated the minimal possible value of these parameters. In this paper, we continue the work in this direction and prove a lower bound for the correlation measure $C_k(E_N)$ (k even) for arbitrary sequences $E_N$, establishing one of their conjectures. We also give an algebraic construction for a sequence $E_N$ with small normality measure N(EN).

AB - Mauduit and Sárközy introduced and studied certain numerical parameters associated to finite binary sequences EN ∈ {-1,1}N in order to measure their 'level of randomness'. Two of these parameters are the normality measure N(EN)$ and the correlation measure $C_k(E_N)$ of order k, which focus on different combinatorial aspects of $E_N$. In their work, amongst others, Mauduit and Sárközy investigated the minimal possible value of these parameters. In this paper, we continue the work in this direction and prove a lower bound for the correlation measure $C_k(E_N)$ (k even) for arbitrary sequences $E_N$, establishing one of their conjectures. We also give an algebraic construction for a sequence $E_N$ with small normality measure N(EN).

UR - http://www.scopus.com/inward/record.url?scp=29744440453&partnerID=8YFLogxK

U2 - 10.1017/S0963548305007170

DO - 10.1017/S0963548305007170

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AN - SCOPUS:29744440453

SN - 0963-5483

VL - 15

SP - 1

EP - 29

JO - Combinatorics Probability and Computing

JF - Combinatorics Probability and Computing

IS - 1-2

ER -