Rank for Some Families of Quaternary Reed-Muller Codes

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• 作者：Jaume Pernas ; Jaume Pujol ; Merc¨¨ Villanueva
• 关键词：Rank ; quaternary codes ; Reed ; Muller codes ; \mathbb Z4\mathbb Z_4 ; linear codes
• 刊名：Lecture Notes in Computer Science
• 出版年：2009
• 出版时间：2009
• 年：2009
• 卷：5527
• 期：1
• 页码：43-52
• 全文大小：231.8 KB

文摘

Recently, new families of quaternary linear Reed-Muller codes such that, after the Gray map, the corresponding ℤ₄-linear codes have the same parameters and properties as the codes in the usual binary linear Reed-Muller family have been introduced. A structural invariant, the rank, for binary codes is used to classify some of these ℤ₄-linear codes. The rank is established generalizing the known results about the rank for ℤ₄-linear Hadamard and ℤ₄-linear extended 1-perfect codes.