On the Rank of Z8-linear Hadamard Codes

Q2 Mathematics
Cristina Fernández-Córdoba, Carlos Vela, Mercè Villanueva
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引用次数: 1

Abstract

The Z2s-additive codes are subgroups of Z2sn, and can be seen as a generalization of linear codes over Z2 and Z4. A Z2s-linear Hadamard code is a binary Hadamard code which is the Gray map image of a Z2s-additive code. It is known that either the rank or the dimension of the kernel can be used to give a complete classification for the Z4-linear Hadamard codes. However, when s>2, the dimension of the kernel of Z2s-linear Hadamard codes of length 2t only provides a complete classification for some values of t and s. In this paper, the rank of these codes is given for s=3. Moreover, it is shown that this invariant, along with the dimension of the kernel, provides a complete classification, once t3 is fixed. In this case, the number of nonequivalent such codes is also established.

关于z8 -线性Hadamard码的秩
z2s -加性码是Z2sn的子群,可以看作是Z2和Z4上线性码的推广。z2s -线性哈达玛码是一种二进制哈达玛码,它是z2s -加性码的灰度图图像。已知核的秩或维数都可以用来给出z4 -线性Hadamard码的完整分类。然而,当s>2时,长度为2t的z2s -线性Hadamard码的核维数仅对t和s的某些值提供了完全分类,本文给出了s=3时这些码的秩。此外,我们还证明,当t≥3固定时,这个不变量与核的维数一起提供了一个完整的分类。在这种情况下,还建立了非等效代码的个数。
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来源期刊
Electronic Notes in Discrete Mathematics
Electronic Notes in Discrete Mathematics Mathematics-Discrete Mathematics and Combinatorics
CiteScore
1.30
自引率
0.00%
发文量
0
期刊介绍: Electronic Notes in Discrete Mathematics is a venue for the rapid electronic publication of the proceedings of conferences, of lecture notes, monographs and other similar material for which quick publication is appropriate. Organizers of conferences whose proceedings appear in Electronic Notes in Discrete Mathematics, and authors of other material appearing as a volume in the series are allowed to make hard copies of the relevant volume for limited distribution. For example, conference proceedings may be distributed to participants at the meeting, and lecture notes can be distributed to those taking a course based on the material in the volume.
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