Table I
Expected Error Signal for an m Sequence
x  1   2   3   4   5   6   7  E(S) 

∑f(x)  1   1   1   0   1   0   0  
− f(x − 0) =  1   1   1   0   1   0   0  
E(S_{t}_{=0}) =  0  +  0  +  0  +  0  +  0  +  0  +  0  = 0 
∑f(x)  1   1   1   0   1   0   0  
− f(x − 1) =  0   1   1   1   0   1   0  
E(S_{t}_{=1}) =  1  +  0  +  0  +  1  +  1  +  1  +  0  = 4 
∑f(x)  1   1   1   0   1   0   0  
− f(x − 2) =  0   0   1   1   1   0   1  
E(S_{t}_{=2}) =  1  +  1  +  0  +  1  +  0  +  0  +  1  = 4 
∑f(x)  1   1   1   0   1   0   0  
− f(x − 3) =  1   0   0   1   1   1   0  
E(S_{t}_{=3}) =  0  +  1  +  1  +  1  +  0  +  1  +  0  = 4 
∑f(x)  1   1   1   0   1   0   0  
− f(x − 4) =  0   1   0   0   1   1   1  
E(S_{t}_{=4}) =  1  +  0  +  1  +  0  +  0  +  1  +  1  = 4 
∑f(x)  1   1   1   0   1   0   0  
− f(x − 5) =  1   0   1   0   0   1   1  
E(S_{t}_{=5}) =  0  +  1  +  0  +  0  +  1  +  1  +  1  = 4 
∑f(x)  1   1   1   0   1   0   0  
− f(x − 6) =  1   1   0   1   0   0   1  
E(S_{t}_{=6}) =  0  +  0  +  1  +  1  +  1  +  0  +  1  = 4 
$E({S}_{t})={\displaystyle \sum _{x=1}^{7}}\mid f(x)f(xt)\mid $ 
Table II
An m′ Sequence with Two Related m Sequences
m sequence (n = 7):  1  1  1  0  1  0  0  
m′ sequence (n = 14):  1  0  1  0  1  0  0  1  1  0  0  1  0  1  
m sequence (n = 15):  1  1  1  1  0  0  0  1  0  0  1  1  0  1  0 
Table III
Probabilities of Misalignment
t  E(S)_{m}  E(S)_{m}′  z_{m}  z_{m}′  p_{m}  p_{m}′  (1 − p_{m})  (1 − p_{m}′)  tp_{m}  tp_{m}′ 

1  8  10  0.566  0.707  0.2857  0.2398  0.7143  0.7602  0.2857  0.2398 
2  16  20  1.131  1.414  0.1290  0.0787  0.8710  0.9213  0.2580  0.1574 
3  24  30  1.697  2.121  0.0449  0.0170  0.9551  0.9830  0.1347  0.0510 
4  32  40  2.263  2.828  0.0118  0.0023  0.9882  0.9977  0.0472  0.0092 
5  40  50  2.828  3.536  0.0023  0.0002  0.9977  0.9998  0.0115  0.0010 
6  48  60  3.394  4.243  0.0004  0.0000  0.9996  1.0000  0.0024  0.0000 
7  56  70  3.960  4.950  0.0000  0.0000  1.0000  1.0000  0.0000  0.0000 
8  64  80  4.525  5.657  0.0000  0.0000  1.0000  1.0000  0.0000  0.0000 
9  72  90  5.091  6.364  0.0000  0.0000  1.0000  1.0000  0.0000  0.0000 
10  81  100  5.728  7.071  0.0000  0.0000  1.0000  1.0000  0.0000  0.0000 
Probability of alignment      0.5856  0.6867   
Probability of misalignment      0.4144  0.3133   
Mean error = ∑tp        0.7395  0.4584 
t: number of sample points by which a pattern is displaced from its aligned position.
E(
S)
_{m}: error signal expected when the
m sequence is misaligned by
t.
z_{m}: E(
S)
_{m}, rendered in standard units by dividing it by the standard error of the difference between the error signal
S_{t} when the pattern is displaced by
t and the error signal
S_{0} when the pattern is aligned.
p_{m}: the probability that
S_{t} will be less than
S_{0}; therefore, the probability that the pattern will be misaligned by
t.
(1 −
p_{m}): the probability that the pattern will
not be misaligned by the distance
t. The probability that the pattern will be correctly aligned (i.e.,
t = 0) is the joint probability that it will not be misaligned at each possible nonzero value of
t. Therefore, the probability of alignment is the product of (1 −
p_{m}) for all values of
t.
The subscript
m′ indicates that the variable subscripted applied to an
m′ sequence instead of an
m sequence.
Table IV
Significant Expected Values of m and m′ Sequences
 m Sequence  m′ Sequence 



p = 2  p > 2 

E(S_{t}_{=0})  0  0  0 
E(S_{t}_{=1}) 
$\frac{n+1}{2}$ 
$\frac{3{n}_{2}}{4}\frac{k}{2}$ 
${n}_{p}\left(1\frac{1}{2p}\right)\frac{k}{2}$ 
E(S_{t}_{=2}) 
$\frac{n+1}{2}$ 
$\frac{{n}_{2}}{2}+k$ 
$\frac{{n}_{p}}{p}+k$ 
μ^{(′)} = E(S_{t}_{≠0})_{min} 
$\frac{n+1}{2}$ 
$\frac{{n}_{2}}{2}k$ 
$\frac{{n}_{p}}{p}+k$ 
$\frac{{\mu}^{\prime}}{\mu}$  
$\frac{3}{2}\frac{k+3}{n+1}$ 
$2\frac{1}{p}\frac{2p+k1}{n+1}$ 