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Questions tagged [gray-code]

For questions about Gray codes, also known as reflected binary codes. It is a binary numeral system where two successive values differ in only one bit (binary digit).

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Decimal convert to Gray Code and 8 4 -2 -1 code

I have tried to convert decimal number with decimal points 67.875 to 8 4 -2 -1 code and Gray code and I got 10101001.100010011011 for 8 4 -2 -1 code and 1100010.100 for Gray code. However, I am not ...
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34 views

Efficient generation of Gray code differences?

We know that the integers $1\le k\le 2^n-1$ (which for the purposes of this post may be identified with their binary expansions) can be mapped to their Gray code equivalents with $k \oplus (k >> ...
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How to generate Maximum Min-SW gray code?

I'm trying to generate Maximum min-SW gray code for structured light described in this paper. Can someone help to understand how to generate this 10 bit gray code?
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Need help with Udi Manber's induction proof for Gray Codes

So, I'm working through Udi Manber's Introduction to Algorithms: A Creative Approach and I cannot wrap my head around his induction-based proof for Gray Codes for odd n. Does anyone have an idea about ...
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44 views

Polynomial-time algorithm to generate the “opposite” of a binary Gray code?

I'm seeking to implement a function $\phi(n,k,i)$ of integers $n,k,i$ where $$1 \leq k < n\\1 \leq i \leq N\\N = {n \choose k}$$ that returns all possible $n$-element binary vectors containing $k$ $...
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59 views

Gray codes over strings of length n?

For any natural number n, an ordering of all binary strings of length n is a Gray code if it starts with 0^n, and any successive strings in the ordering differ in exactly one bit (the first and last ...
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29 views

Justify a Linear code

Consider the code $C=\{0000, 0010, 0020, abcd, 2110, 2100, 1220, 2120, 1210\}\subset F^{4}_3$ To determine $abcd\in F^{4}_3$ for $C$ to be linear is to say that $abcd$ is a linear combination of a ...
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230 views

Determine the immediate successors of the following 9-tuple in the reflected Gray Code of order 9.

Problem: Determine the immediate successors of the following 9-tuple in the reflected Gray Code of order 9. $$111111111.$$ My Attempt: I am using the following algorithm to solve this problem: ...