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Abstract The Gray Code
, 2007
"... This report is a selfcontained summary of properties and algorithms concerning the Gray code. Descriptions are given of the Gray code definition, algorithms and circuits for generating the code and for conversion between binary and Gray code, for incrementing, counting, and adding Gray code words. ..."
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Cited by 5 (0 self)
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This report is a selfcontained summary of properties and algorithms concerning the Gray code. Descriptions are given of the Gray code definition, algorithms and circuits for generating the code and for conversion between binary and Gray code, for incrementing, counting, and adding Gray code words
The Gray Code 1
"... Abstract: Here we summarise the properties and algorithms of the Gray code. Descriptions are given of the Gray code definition, algorithms and circuits for generating the code and for conversion between binary and Gray code, for incrementing, counting, and adding Gray code words. Some interesting ap ..."
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Abstract: Here we summarise the properties and algorithms of the Gray code. Descriptions are given of the Gray code definition, algorithms and circuits for generating the code and for conversion between binary and Gray code, for incrementing, counting, and adding Gray code words. Some interesting
A Survey of Combinatorial Gray Codes
 SIAM Review
, 1996
"... The term combinatorial Gray code was introduced in 1980 to refer to any method for generating combinatorial objects so that successive objects differ in some prespecified, small way. This notion generalizes the classical binary reflected Gray code scheme for listing nbit binary numbers so that ..."
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Cited by 123 (2 self)
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The term combinatorial Gray code was introduced in 1980 to refer to any method for generating combinatorial objects so that successive objects differ in some prespecified, small way. This notion generalizes the classical binary reflected Gray code scheme for listing nbit binary numbers so
Graphs induced by Gray codes
 Discrete Math
"... Abstract. We disprove a conjecture ofBultena and Ruskey [1], that all trees which are cyclic graphs ofcyclic Gray codes have diameter 2 or 4, by producing codes whose cyclic graphs are trees ofarbitrarily large diameter. We answer affirmatively two other questions from [1], showing that strongly Pn ..."
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Cited by 3 (0 self)
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Abstract. We disprove a conjecture ofBultena and Ruskey [1], that all trees which are cyclic graphs ofcyclic Gray codes have diameter 2 or 4, by producing codes whose cyclic graphs are trees ofarbitrarily large diameter. We answer affirmatively two other questions from [1], showing that strongly Pn
Balanced Gray Codes
 ELECTRONIC J. COMBINATORICS
, 1996
"... It is shown that balanced nbit Gray codes can be constructed for all positive integers n. A balanced Gray code is one in which the bit changes are distributed as equally as possible among the bit positions. The strategy used is to prove the existence of a certain subsequence which will allow suc ..."
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Cited by 11 (2 self)
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It is shown that balanced nbit Gray codes can be constructed for all positive integers n. A balanced Gray code is one in which the bit changes are distributed as equally as possible among the bit positions. The strategy used is to prove the existence of a certain subsequence which will allow
Antipodal Gray Codes
 Discrete Mathematics
, 2002
"... An nbit Gray code is a circular listing of the 2 nbit strings so that successive strings dier only in one bit position. An nbit antipodal Gray code has the additional property that the complement of any string appears exactly n steps away in the list. The problem of determining for which values ..."
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Cited by 1 (0 self)
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An nbit Gray code is a circular listing of the 2 nbit strings so that successive strings dier only in one bit position. An nbit antipodal Gray code has the additional property that the complement of any string appears exactly n steps away in the list. The problem of determining for which
The Graycode filter kernels
 IEEE Trans. Pattern Anal. Mach. Intell
, 2007
"... Abstract In this paper we introduce a family of filter kernels the GrayCode Kernels (GCK) and demonstrate their use in image analysis. Filtering an image with a sequence of GrayCode Kernels is highly efficient and requires only 2 operations per pixel for each filter kernel, independent of the si ..."
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Cited by 18 (1 self)
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Abstract In this paper we introduce a family of filter kernels the GrayCode Kernels (GCK) and demonstrate their use in image analysis. Filtering an image with a sequence of GrayCode Kernels is highly efficient and requires only 2 operations per pixel for each filter kernel, independent
Gray Codes for Reflectable Languages
, 2008
"... We classify a type of language called a reflectable language. We then develop a generic algorithm that can be used to list all strings of length n for any reflectable language in Gray code order. The algorithm generalizes Gray code algorithms developed independently for kary strings, restricted gro ..."
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Cited by 4 (2 self)
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We classify a type of language called a reflectable language. We then develop a generic algorithm that can be used to list all strings of length n for any reflectable language in Gray code order. The algorithm generalizes Gray code algorithms developed independently for kary strings, restricted
Gray code compression
"... An nbit (cyclic) Gray code is a (cyclic) sequence of all nbit strings such that consecutive strings differ in a single bit. We describe an algorithm which for every positive integer n constructs an nbit cyclic Gray code whose graph of transitions is the ddimensional hypercube Qd if n = 2 d, or ..."
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An nbit (cyclic) Gray code is a (cyclic) sequence of all nbit strings such that consecutive strings differ in a single bit. We describe an algorithm which for every positive integer n constructs an nbit cyclic Gray code whose graph of transitions is the ddimensional hypercube Qd if n = 2 d
Shift Gray Codes
, 2009
"... Combinatorial objects can be represented by strings, such as 21534 for the permutation (1 2) (3 5 4), or 110100 for the binary tree corresponding to the balanced parentheses (()()). Given a string s = s1s2⋯sn, the rightshift operation ��→ shift(s, i, j) replaces the substring sisi+1⋯sj by si+1⋯sjsi ..."
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Cited by 7 (4 self)
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fixedcontent language, a shift Gray code is a list of its strings where consecutive strings differ by a shift. This thesis asks if shift Gray codes exist for a variety of combinatorial objects. This abstract question leads to a number of practical answers. The first prefixshift Gray code for multiset
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