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Classification of Some Families of Quaternary Reed–Muller Codes

✍ Scribed by Pernas, J.; Pujol, J.; Villanueva, M.

Book ID: 114642599
Publisher: IEEE
Year: 2011
Tongue: English
Weight: 279 KB
Volume: 57
Category: Article
ISSN: 0018-9448
DOI: 10.1109/tit.2011.2119465

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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