New family of binary sequences of period 4(2n − 1) with low correlation

A new family of binary sequences of period 4(2n−1) with low correlation is constructed for integer n = em. Especially, we obtain a new family with family size 2n and maximum nontrivial correlation magnitude $${2^{n+3\over 2}+4}$$ for odd m and e = 1. Each sequence in the family is constructed by the interleaving of four GKW-like sequences and a perfect sequence. The correlation distribution and linear spans of the sequences are also determined for odd m.

[1]  Rudolf Lide,et al.  Finite fields , 1983 .

[2]  A. Nechaev,et al.  Kerdock code in a cyclic form , 1989 .

[3]  Pingzhi Fan,et al.  Generalized binary Udaya-Siddiqi sequences , 2004, ISIT.

[4]  Jong-Seon No,et al.  New families of binary sequences with low correlation , 2003, IEEE Trans. Inf. Theory.

[5]  K. Conrad,et al.  Finite Fields , 2018, Series and Products in the Development of Mathematics.

[6]  Lloyd R. Welch,et al.  Lower bounds on the maximum cross correlation of signals (Corresp.) , 1974, IEEE Trans. Inf. Theory.

[7]  Tadao Kasami,et al.  The Weight Enumerators for Several Clauses of Subcodes of the 2nd Order Binary Reed-Muller Codes , 1971, Inf. Control..

[8]  M. U. Siddiqi,et al.  hase Sequences with Large Linear erived from Sequences over 24 , 1996 .

[9]  Guang Gong,et al.  New designs for signal sets with low cross correlation, balance property, and largelinear span: GF(p) case , 2002, IEEE Trans. Inf. Theory.

[10]  Jong-Seon No,et al.  A new family of binary pseudorandom sequences having optimal periodic correlation properties and large linear span , 1988, IEEE International Conference on Communications, - Spanning the Universe..

[11]  P. Vijay Kumar,et al.  Binary sequences with Gold-like correlation but larger linear span , 1994, IEEE Trans. Inf. Theory.

[12]  P. Vijay Kumar,et al.  A new family of binary pseudorandom sequences having optimal periodic correlation properties and large linear span , 1989, IEEE Trans. Inf. Theory.

[13]  Leslie R. Welch.  Lower bounds on the maximum correlation of signals , 1974 .

[14]  Guang Gong,et al.  Signal Design for Good Correlation: For Wireless Communication, Cryptography, and Radar , 2005 .

[15]  Robert Gold,et al.  Maximal recursive sequences with 3-valued recursive cross-correlation functions (Corresp.) , 1968, IEEE Trans. Inf. Theory.

[16]  Robert A. Scholtz,et al.  Bent-function sequences , 1982, IEEE Trans. Inf. Theory.