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Convert mask vector to shift for shift register configuration

## Description

shift = mask2shift(prpoly,mask) returns the shift that is equivalent to a mask, for a linear feedback shift register whose connections are specified by the primitive polynomial prpoly. The prpoly input can have one of these formats:

• A binary vector that lists the coefficients of the primitive polynomial in order of descending powers

• An integer scalar whose binary representation gives the coefficients of the primitive polynomial, where the least significant bit is the constant term

The mask input is a binary vector whose length is the degree of the primitive polynomial.

 Note:   To save time, mask2shift does not check that prpoly is primitive. If it is not primitive, the output is not meaningful. To find primitive polynomials, use primpoly or see [2].

### Definition of Equivalent Shift

If A is a root of the primitive polynomial and m(A) is the mask polynomial evaluated at A, the equivalent shift s solves the equation As = m(A). To interpret the vector mask as a polynomial, treat mask as a list of coefficients in order of descending powers.

## Examples

The first command below converts a mask of x3 + 1 into an equivalent shift for the linear feedback shift register whose connections are specified by the primitive polynomial x4 + x3 + 1. The second command shows that a mask of 1 is equivalent to a shift of 0. In both cases, notice that the length of the mask vector is one less than the length of the prpoly vector.

s = mask2shift([1 1 0 0 1],[1 0 0 1])
s2 = mask2shift([1 1 0 0 1],[0 0 0 1])

The output is below.

s =

4

s2 =

0

## References

[1] Lee, J. S., and L. E. Miller, CDMA Systems Engineering Handbook, Boston, Artech House, 1998.

[2] Simon, Marvin K., Jim K. Omura, et al., Spread Spectrum Communications Handbook, New York, McGraw-Hill, 1994.