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On the covering radius of Reed-Muller codes

✍ Scribed by Gérard D. Cohen; Simon N. Litsyn

Publisher
Elsevier Science
Year
1992
Tongue
English
Weight
371 KB
Volume
106-107
Category
Article
ISSN
0012-365X

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✦ Synopsis

We present lower and upper bounds on the covering radius of Reed-Muller codes, yielding asymptotical improvements on known results. The lower bound is simply the sphere covering one (not very new). The upper bound is derived from a thorough use of a lemma, the 'essence of Reed-Mullerity'.

The idea is to find a 'seed' upper bound-a properly chosen combination of binomial coefficients-well fitted to the respective growths of m (log of length) and r (order), to initiate double induction on m and r. Surprisingly enough, these two simple ingredients s&ice to essentially fill the gaps between lower and upper bounds, a result stated in our theorem.

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