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A computability challenge: asymptotic bounds and isolated error-correcting codes
asymptotic bounds isolated error-correcting codes Information Theory
2011/7/21
Abstract: Consider the set of all error--correcting block codes over a fixed alphabet with $q$ letters. It determines a recursively enumerable set of points in the unit square with coordinates $(R,\de...
On optimal asymptotic bounds for spherical designs
spherical designs fixed point theorems Marcinkiewicz–Zygmund inequality area-regular partitions
2010/9/1
For each N ≥ cdtd we prove the existence of a spherical t-design on the sphere Sd consisting of N points, where cd is a constant depending only on d. This result proves the well-known conjecture of Ko...