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The covering radius of the Reed-Muller code is at least 16276

✍ Scribed by Patterson, N.; Wiedemann, D.

Book ID
114635281
Publisher
IEEE
Year
1983
Tongue
English
Weight
349 KB
Volume
29
Category
Article
ISSN
0018-9448

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πŸ“œ SIMILAR VOLUMES

On the covering radius of Reed-Muller co
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✍ GΓ©rard D. Cohen; Simon N. Litsyn πŸ“‚ Article πŸ“… 1992 πŸ› Elsevier Science 🌐 English βš– 371 KB

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

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✍ Xiang-Dong Hou πŸ“‚ Article πŸ“… 1992 πŸ› Springer 🌐 English βš– 312 KB

Let R(r, m) be the rth order Reed-Muller code of length 2 '~, and let p(r, m) be its covering radius. We prove that if 2 \_< k -< m -r -1, then p(r + k, m + k) > #(r, m) + 2(k -1). We also prove that if m -r > 4, 2 < k < m -r -1, and R(r, m) has a coset with minimal weight pfr, m) which does not co