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On Z8-Linear Hadamard Codes: Rank and Classification.
- Source :
-
IEEE Transactions on Information Theory . Feb2020, Vol. 66 Issue 2, p970-982. 13p. - Publication Year :
- 2020
-
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]
Details
- Language :
- English
- ISSN :
- 00189448
- Volume :
- 66
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- IEEE Transactions on Information Theory
- Publication Type :
- Academic Journal
- Accession number :
- 141381306
- Full Text :
- https://doi.org/10.1109/TIT.2019.2952599