2022/03/29 by Dipak K. Bhunia, Bhunia, Dipak K., Cristina Fernández-Córdoba +5
Computer Science · Engineering · #Coding theory and cryptography #graph theory and CDMA systems #Cooperative Communication and Network Coding
paper · pdf · doi:10.48550/arxiv.2203.15407
The \Zps-additive codes of length n are subgroups of \Zpsn, and can be seen as a generalization of linear codes over \Z2, \Z4, or \Z2s in general. A \Zps-linear generalized Hadamard (GH) code is a GH code over \Zp which is the image of a \Zps-additive code by a generalized Gray map. A partial classification of these codes by using the dimension of the kernel is known. In this paper, we establish that some \Zps-linear GH codes of length pt are equivalent, once t is fixed. This allows us to improve the known upper bounds for the number of such nonequivalent codes. Moreover, up to t=10, this new upper bound coincides with a known lower bound (based on the rank and dimension of the kernel).