nCk sequences and their difference sequences
Asbj{\o}rn Br{\ae}ndeland
TL;DR
This paper introduces a method to efficiently generate nCk sequences and their difference sequences, leveraging regularities to achieve faster computation times.
Contribution
It presents a novel approach to generate nCk sequences and their difference sequences in linear time, improving efficiency over previous methods.
Findings
Difference sequences exhibit regularities enabling quick generation.
nCk sequences can be generated in linear time using the proposed method.
The approach significantly reduces computational complexity.
Abstract
A nCk sequence is a sequence of n-bit numbers with k bits set. Given such a sequence C, the difference sequence D of C is subject to certain regularities that make it possible to generate D in 2|C| time, and, hence, to generate C in 3|C| time.
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Taxonomy
Topicsgraph theory and CDMA systems · Coding theory and cryptography · Advanced Signal Processing Techniques