Method for generation of even numbered reduced gray codes

Details Method for generation of even numbered reduced gray codes Method for generation of even numbered reduced gray codes

2005-11-29

2005-11-29

Jeanpierre, Peguy (Department: 2819)

Coded data generation or conversion

Digital code to digital code converters

To or from constant distance codes

C375S242000

Reexamination Certificate

active

06970113

ABSTRACT:
A cyclic reduced Gray code in n-many bits having 2k-many entries, for any natural number k, where 2(n−1)<2k<2nand n is a positive integer, is found by first constructing a 2n-many entry code in n-many bits with a reflected binary technique, and then selecting the last k-many ordered entries in the first half of the full reflected binary code, followed by the first k-many ordered entries in the second half of the full reflected binary code. These ordered 2k-many entries are a shortened cyclic reduced Gray code in n-many bits. Alternatively, the first k-many ordered entries in the first half of the full reflected binary code can be selected, followed by the last k-many ordered entries in the second half of the full reflected binary code. If either the original or reduced Gray code is expressed as a table whose columns are bit positions and whose rows are the code entries, then entire columns can optionally be interchanged at will, either before or after the 2k-many selection, to produce additional different cyclic reduced Gray codes that do not outwardly appear to be ‘reflected’ ones.

REFERENCES:
patent: 2632058 (1953-03-01), Gray
patent: 4101882 (1978-07-01), Kramer
patent: 4146873 (1979-03-01), Yamanaka et al.
patent: 5969895 (1999-10-01), Ueda et al.
patent: 6703950 (2004-03-01), Yi

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