COMPLEXITY OF ELIAS ALGORITHM BASED ON CODES WITH COVERING RADIUS THREE

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Submitted: 2025-02-18; Published: 2025-02-18

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Abstract

The algorithm for finding the set of ”nearest neighbors” in a set using compact blocks and hash functions is known (Elias algorithm). In this paper hash coding schemas associated to coverings by spheres of the same radius are considered. In general, such coverings can be obtained via perfect codes, and some other generalizations of perfect codes such as uniformly packed or quasi perfect codes. We consider the mentioned algorithm for Golay code and for two-error-correcting primitive BCH codes of lenght 2m−1 for odd m. A formula of time complexity of the algorithm is obtained in these cases.