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Constructive Spherical Codes near the Shannon Bound

Abstract : Shannon gave a lower bound in 1959 on the binary rate of spherical codes of given minimum Euclidean distance p. Using nonconstructive codes over a finite alphabet, we give a lower bound that is weaker but very close for small values of p. The construction is based on the Yaglom map combined with some finite sphere packings obtained from nonconstructive codes for the Euclidean metric. Concatenating geometric codes meeting the TVZ bound with a Lee metric BCH code over GF(p); we obtain spherical codes that are polynomial time constructible. Their parameters outperform those obtained by Lachaud and Stern in 1994. At very high rate they are above 98 per cent of the Shannon bound.
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https://hal.inria.fr/inria-00614479
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Submitted on : Thursday, August 11, 2011 - 4:16:49 PM
Last modification on : Saturday, November 14, 2020 - 7:06:03 PM
Long-term archiving on: : Monday, November 12, 2012 - 3:21:57 PM

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  • HAL Id : inria-00614479, version 1

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Patrick Solé, Jean-Claude Belfiore. Constructive Spherical Codes near the Shannon Bound. WCC 2011 - Workshop on coding and cryptography, Apr 2011, Paris, France. pp.453-462. ⟨inria-00614479⟩

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