New families of biphase sequences of size 2T-1 + I, r being a positive integer, are derived from families of in- terleaved maximal-length sequences over 24 of period 2(Zr - 1). These sequences have applications in code-division spread- spectrum multiuser communication systems. The families satisfy Sidelnikov bound with equality on Omax, which denotes the maximum magnitude of the periodic crosscorreslation and out-of- phase antocorrelatiou values. One of the families satisfies Welch bound on Om,, with equality. The linear complexity and the period of all sequences are equal to T(T + 3)/2 and 2(2' - l), respectively, with an exception of the single m-sequence which has linear complexity r and period 2' - 1. Sequence imbalance and correlation distributions are also computed.
[1]
P. Vijay Kumar,et al.
4-phase Sequences with Near-optimum Correlation Properties
,
1992,
IEEE Trans. Inf. Theory.
[2]
A. Nechaev,et al.
Kerdock code in a cyclic form
,
1989
.
[3]
Rudolf Lide,et al.
Finite fields
,
1983
.
[4]
I. Herstein,et al.
Topics in algebra
,
1964
.
[5]
B. R. McDonald.
Finite Rings With Identity
,
1974
.
[6]
Dilip V. Sarwate,et al.
Quadriphase sequences for spread-spectrum multiple-access communication
,
1984,
IEEE Trans. Inf. Theory.
[7]
R. Raghavendran,et al.
Finite associative rings
,
1969
.