Rank and Pairs of Rank and Dimension of Kernel of Z p Z p ²-Linear Codes
Xiaoxiao Li, Minjia Shi, Shukai Wang, Haodong Lu, Yuxuan Zheng · IEEE Transactions on Information Theory · 2023
A code$C$is called$Z_{p}Z_{p^{2}}$-linear if it is the Gray image of a$Z_{p}Z_{p^{2}}$-additive code. For any prime number$p$larger than 3, the bounds of the rank of$Z_{p}Z_{p^{2}}$-linear codes are given. For each value of the rank and the pairs of rank and the dimension of the kernel of$Z_{p}Z_{p^{2}}$-linear codes, we give detailed construction of the corresponding codes. As an example, the rank and the dimension of the kernel of$Z_{5}Z_{25}$-linear codes are studied.