Gray Codes for AT-Free Orders via Antimatroids

2016 ◽  
pp. 77-87 ◽  
Author(s):  
Jou-Ming Chang ◽  
Ton Kloks ◽  
Hung-Lung Wang
Keyword(s):  
Gray Codes

On locally balanced gray codes

2016 ◽  
Vol 10 (1) ◽  
pp. 78-85 ◽  
Author(s):  
I. S. Bykov
Keyword(s):  
Gray Codes

A PARALLEL ALGORITHM TO GENERATE N-ARY REFLECTED GRAY CODES IN A LINEAR ARRAY WITH RECONFIGURABLE BUS SYSTEM

1993 ◽  
Vol 03 (02) ◽  
pp. 157-164 ◽  
Author(s):  
P. THANGAVEL ◽  
V.P. MUTHUSWAMY
Keyword(s):  
Parallel Algorithm ◽  
Linear Array ◽  
Constant Time ◽  
Processor Array ◽  
Gray Codes ◽  
System A ◽  
Processor Arrays ◽  
Bus System

A simple parallel algorithm for generating N-ary reflected Gray codes is presented. The algorithm is derived from the pattern of N-ary reflected Gray codes. The algorithm runs on a linear processor array with a reconfigurable bus system. A reconfigurable bus system is a bus system whose configuration can be dynamically changed. Recently processor arrays with reconfigurable bus systems were used to solve many problems in constant time. There already exists experimental reconfigurable chips.

scholarly journals Balancing Cyclic $R$-ary Gray Codes

10.37236/949 ◽  
2007 ◽  
Vol 14 (1) ◽  
Author(s):  
Mary Flahive ◽  
Bella Bose
Keyword(s):  
Gray Codes

New cyclic $n$-digit Gray codes are constructed over $\{0, 1, \ldots, R-1 \}$ for all $R \ge 3$, $n \ge 2$. These codes have the property that the distribution of the digit changes (transition counts) is close to uniform: For each $n \ge 2$, every transition count is within $R-1$ of the average $R^n/n$, and for the $2$-digit codes every transition count is either $\lfloor{R^2/2} \rfloor$ or $\lceil{R^2/2} \rceil$.

Near optimal single-track Gray codes

1996 ◽  
Vol 42 (3) ◽  
pp. 779-789 ◽  
Author(s):  
T. Etzion ◽  
K.G. Paterson
Keyword(s):  
Gray Codes ◽  
Single Track

scholarly journals Permutational labelling of constant weight Gray codes

2002 ◽  
Vol 65 (3) ◽  
pp. 399-406
Author(s):  
Inessa Levi ◽  
Steve Seif
Keyword(s):  
Gray Code ◽  
Gray Codes ◽  
Constant Weight ◽  
Single Exception ◽  
Positive Integers

We prove that for positive integers n and r satisfying 1 < r < n, with the single exception of n = 4 and r = 2, there exists a constant weight Gray code of r-sets of Xn = {1, 2, …, n} that admits an orthogonal labelling by distinct partitions, with each subsequent partition obtained from the previous one by an application of a permutation of the underlying set. Specifically, an r-set A and a partition π of Xn are said to be orthogonal if every class of π meets A in exactly one element. We prove that for all n and r as stated, and taken modulo , there exists a list of the distinct r-sets of Xn with |Ai ∩ Ai+1| = r − 1 and a list of distinct partitions such that πi is orthogonal to both Ai and Ai+1, and πi+1 = πiλi for a suitable permutation λi of Xn.

scholarly journals Absolute Position Coding Method for Angular Sensor—Single-Track Gray Codes

Sensors ◽  
2018 ◽  
Vol 18 (8) ◽  
pp. 2728 ◽  
Author(s):  
Fan Zhang ◽  
Hengjun Zhu ◽  
Kan Bian ◽  
Pengcheng Liu ◽  
Jianhui Zhang
Keyword(s):  
Coding Theory ◽  
Linear Feedback ◽  
Gray Codes ◽  
Single Track ◽  
Absolute Position ◽  
Coding Method ◽  
Position Coding ◽  
Absolute Encoder ◽  
Feedback Shift Register ◽  
Generating Sequences

Single-track Gray codes (STGCs) is a type of absolute position coding method for novel angular sensors, because it has single-track property over traditional Gray codes and mono-difference over linear feedback shift register codes. However, given that the coding theory of STGCs is incomplete, STGC construction is still a challenging task even though it has been defined for more than 20 years. Published coding theories and results on STGCs are about two types of STGC, namely, necklace and self-dual necklace ordering, which are collectively called as k-spaced head STGCs. To find a new code, three constraints on generating sequences are proposed to accelerate the searching algorithm, and the complete searching result of length-6 STGCs is initially obtained. Among the entire 132 length-6 STGCs, two novel types of STGCs with non-k-spaced heads are found, and the basic structures of these codes with the general length n are proposed and defined as twin-necklace and triplet-necklace ordering STGCs. Furthermore, d-plet-necklace ordering STGC, which unifies all the known STGCs by changing the value of d, is also defined. Finally, a single-track absolute encoder prototype is designed to prove that STGCs are as convenient as the traditional position coding methods.

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