1. On Z8-Linear Hadamard Codes: Rank and Classification.
- Author
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Fernandez-Cordoba, Cristina, Vela, Carlos, and Villanueva, Merce
- Subjects
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HADAMARD codes , *LINEAR codes , *BINARY codes , *CLASSIFICATION , *ERROR correction (Information theory) , *LINEAR algebraic groups - Abstract
The Z2s-additive codes are subgroups of Zn2s, 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 computed for s = 3. Moreover, it is proved that this invariant, along with the dimension of the kernel, provides a complete classification, once t ≥ 3 is fixed. In this case, the number of nonequivalent such codes is also established. [ABSTRACT FROM AUTHOR]
- Published
- 2020
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