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Golay Code Clustering Using Double Golay Encoding Technique Open Access

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In traditional error-correction schemes, a certain number of parity bits are added to a data word to compose a codeword. If a certain number of distortions happen during transmission, the redundant parity bits can be used to restore the original data word. If there is an exhaustive correspondence between codeword space and data word space, we may be able to build a clustering system based on the special error-correction relationship between the codeword space and the data word space. The concept of our clustering algorithm comes from a reverse of the traditional error-correction scheme using the perfect Golay code (23, 12, 7).The purpose of this dissertation is to develop a new clustering data structure and a novel navigation mechanism over the clustering systems. The primary technique we use here is double Golay encoding. Golay code is the only useful perfect code. It has a one-to-one corresponding relationship between data word and codeword. The codeword pool is big enough to satisfy our clustering purpose. Moreover, the result clusters construct a new data structure. The new data structure provides incredible clear boundaries between clusters. It works with double Golay encoding together to make flexible navigation among clusters become feasible.

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