Feedback shift register with states decomposed into cycles of equal length

Claim 2

A feedback shift register comprising: a shift register of n stages arranged in a sequence with the first stage in said sequence representing an input stage, each stage being in either a binary 1 state or a binary 0 state and capable of providing an output indicative of its state; mod-2 adding means coupled to y selected stages of said register, for providing an output representing the complement of the mod-2 addition of the outputs of said y stages, y<n and y being always odd and comprising stages in said sequence which correspond to exponents of terms X in the expansion of the expression (X+1)n; and means for for directly supplying the output of said mod-2 adding means to the input stage of said shift register.

Claim 3

The arrangement as recited in claim 1 wherein n is not equal to a power of 2 and whereby the outputs of said n stages define disjointed multiword cycles, where complementary words appear in different cycles, each cycle including 2i words, where i and n are related by the expression 2i 1<n+1< 2i.

Claim 4

The arrangement as recited in claim 1 wherein n is equal to a power of 2 and the outputs of said n stages define multiword cycles, where complementary words appear in the same cycle, 180* apart, and each cycle includes 2i words where n and i are related by the expression, 2i 1<n+1<2i.

Claim 5

The arrangement as recited in claim 1 wherein the output of the highest order stage in said shift register is connected to said mod-2 adding means.

Claim 6

The arrangement as recited in Claim 1 wherein the outputs of said n stages define multiword cycles, each cycle comprising 2i words, where i and n are related by the expression 2i 1<n+1<2i.

Claim 7

A feedback shift register comprising: a shift register of n stages arranged in a sequence with the first stage in said sequence representing an input stage and the stage opposite said input stage in said sequence representing a last stage, each stage being in either a binary 1 state or a binary 0 state and capable of providing an output indicative of its state; mod-2 adding means coupled to y selected stages of said register for providing an output representing the complement of the mod-2 addition of the outputs of said y stages, said y stages including the last stage, y<n, y equaling 1 less than 2 raised to the power of a number which represents the number of 1''s in the binary representation of n; and means for supplying the output of said mod-2 adding means to the input of the input stage of said shift register.

Claim 8

A feedback shift register comprising: a shift register of n stages arranged in a sequence with the first stage in said sequence representing an input stage and the stage opposite said input stage in said sequence representing a last stage, each stage being in either a binary 1 state or a binary 0 state and capable of providing an output indicative of its state; mod-2 adding means coupled to y selected stages of said register for providing an output representing the complement of the mod-2 addition of the outputs of said y stages, said y stages including the last stage, y<n, y equaling 1 less than 2 raised to the power of a number which represents the number of 1''s in the binary representation of n; and means for supplying the output of said mod-2 adding means to the input of the input stage of said shift register.

Claim 9

The arrangement as recited in claim 6 wherein the y stages which are connected to said mod-2 adding means comprise stages in said sequence which correspond to exponents of terms X in the expansion of the expression (X+1)n, in which each expanded expression (X+1)n, in which each expanded expression (X+1)r Xr+1, where r is a power of 2.

Claim 10

The arrangement as recited in claim 7 wherein n is not equal to a power of 2 and whereby the outputs of said n stages define disjointed multiword cycles, where complementary words appear in different cycles, each cycle including 2i words, where i and n are related by the expression 2i 1<n+ 1< 2i.

Claim 11

The arrangement as recited in claim 7 wherein n is equal to a power of 2 and the outputs of said n stage define multiword cycles, where complementary words appear in the same cycle, 180*apart, and each cycle includes 2i words where n and i are related by the expression, 2i 1<n+1< 2i.