Please use this identifier to cite or link to this item:
http://hdl.handle.net/10773/39965
Title: | Equivalences among Zps -linear generalized Hadamard codes |
Author: | Bhunia, Dipak Kumar Fernández-Córdoba, Cristina Villanueva, Mercè Cabello, Carlos Vela |
Keywords: | Generalized Hadamard code Gray map Zps-linear code Rank Kernel Classification |
Issue Date: | 2023 |
Publisher: | CIRM |
Abstract: | Linear codes of length n over Zps, p prime, called Zps-additive codes, can be seen as subgroups of Zn ps. A Zps-linear generalized Hadamard (GH) code is a GH code over Zp which is the image of a Zps-additive code under a generalized Gray map. It is known that the dimension of the kernel allows to classify these codes partially and to establish some lower and upper bounds on the number of such codes. Indeed, in this paper, for p≥3 prime, we establish that some Zps-linear GH codes of length p^t having the same dimension of the kernel are equivalent to each other, once t is fixed. This allows us to improve the known upper bounds. Moreover, up to t=10 if p=3 or t=8 if p=5, this new upper bound coincides with a known lower bound based on the rank and dimension of the kernel. |
Peer review: | yes |
URI: | http://hdl.handle.net/10773/39965 |
Appears in Collections: | DMat - Comunicações |
Files in This Item:
File | Description | Size | Format | |
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CristinaFernandez.pdf | 739.91 kB | Adobe PDF | View/Open |
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