It is proved that for noncan the Hamming space {0, 1}nbe partitioned into three Hamming spheres of any, not necessarily equal radii.
Tight packings with Hamming spheres of equal radius, i.e., packings which are coverings at the same time, are rare and are studied under the name of perfect ...
It is proved that for noncan the Hamming space {0, 1}nbe partitioned into three Hamming spheres of any, not necessarily equal radii.
In geometry, a sphere packing is an arrangement of non-overlapping spheres within a containing space. The spheres considered are usually all of identical ...
Aug 7, 2024 · They pack codewords as tightly as possible ... Hamming bound, emphasizing the geometric interpretation of packing Hamming spheres in a space ...
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Feb 1, 2017 · Although it is widely believed that Gilbert-Varshamov bound is tight, we do not know of any efficient (sub-exponential time) construction of a ...
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Apr 30, 2024 · Four mathematicians broke a 75-year-old record by finding a denser way to pack high-dimensional spheres.
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Oct 3, 2023 · Adopting the concept of contact graph from classical continuous sphere packing problems, a reduction technique for the models is introduced,.
... packing bound is tight: this is by a remarkable algebraic family of codes known as BCH codes. 4. Page 5. 4 The d = 3 case: the Hamming code. For d = 3, the ...
Upon defining -covering and -packing, one naturally asks what is the minimal number of -balls ... Furthermore, for Hamming space and Hamming distance, this is ...