Physical Sciences and Mathematics Commons^™

Cyclic Mixed-Radix Dense Gray Codes, Jessica Cheng

Computer Science Senior Theses

A Gray code is a sequence of n binary integers in the range 0 to n-1 that has the Gray-code property: each integer in the sequence differs from the integer before it in a single digit. Gray codes have many applications, ranging from rotary encoders to Boolean circuit minimization. We refer to Gray codes where the first and last
codewords in the sequence fulfill the Gray-code property as cyclic. Additionally, we refer to a Gray code as dense if the sequence of n numbers consists of a permutation of ⟨0, 1, . . . , n − 1⟩. This thesis …