scholarly journals Gray Codes and Overlap Cycles for Restricted Weight Words

2014 ◽  
Author(s):  
Victoria Horan ◽  
Glenn Hurlbert
Keyword(s):  
Gray Codes ◽  
Overlap Cycles

scholarly journals Gray codes and overlap cycles for restricted weight words

2014 ◽  
Vol 06 (04) ◽  
pp. 1450062
Author(s):  
Victoria Horan ◽  
Glenn Hurlbert
Keyword(s):  
Gray Code ◽  
Existence Results ◽  
Minimal Change ◽  
Gray Codes ◽  
Weight Range ◽  
Combinatorial Objects ◽  
The Past ◽  
Fixed Weight ◽  
New Type ◽  
Overlap Cycles

A Gray code is a listing structure for a set of combinatorial objects such that some consistent (usually minimal) change property is maintained throughout adjacent elements in the list. While Gray codes for m-ary strings have been considered in the past, we provide a new, simple Gray code for fixed-weight m-ary strings. In addition, we consider a relatively new type of Gray code known as overlap cycles and prove basic existence results concerning overlap cycles for fixed-weight and weight-range m-ary words.

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.

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
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