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Some inequalities about the covering radius of Reed-Muller codes

✍ Scribed by Xiang-Dong Hou

Publisher
Springer
Year
1992
Tongue
English
Weight
312 KB
Volume
2
Category
Article
ISSN
0925-1022

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✦ Synopsis

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 contain any vector of weight p(r, m) + 2, then p(r + k, m + k) -> p(r, m) + 2k. These inequalities improve repeated use of the known result p(r + 1, m + 1) >_ p(r, m).

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