Qunying Liao

Zhonghao Liang, Dongmei Huang, Qunying Liao et al.

In recent years, the construction of non-GRS type linear codes has attracted considerable attention due to that they can effectively resist both the Sidelnikov-Shestakov attack and the Wieschebrink attack. Constructing linear complementary dual (LCD) codes and determining the hull of linear codes have long been important topics in coding theory, as they play the crucial role in constructing entanglement-assisted quantum error-correcting codes (EAQECCs), certain communication systems and cryptography. In this paper, by utilizing a class of non-GRS type linear codes, namely, generalized Roth-Lempel (in short, GRL) codes, we firstly construct several classes of Euclidean LCD codes, Hermitian LCD codes, and linear codes with small-dimensional hulls, generalized the main results given by Wu et al. in 2021. We also present an upper bound for the number of a class of Euclidean GRL codes with 1-dimensional hull, and then for several classes of Hermitian GRL codes, we firstly derive an upper bound for the dimension of the hull, and prove that the bound is attainable. Secondly, as an application, we obtain several families of EAQECCs. Thirdly, we prove that the GRL code is non-GRS for $k >\ell$. Finally, some corresponding examples for LCD MDS codes and LCD NMDS codes are presented.

Haibo Liu, Chengzhi Wei, Qunying Liao

In this paper, a class of linear authentication codes with secrecy are constructed, which have simple encoding rules and are easy to implement. Based on the special Weil sum, the maximum success probabilities of substitution attack and impersonation attack are calculated, and these codes are proven to be asymptotically optimal with respect to certain bounds.

Haibo Liu, Xin Guo, Qunying Liao

Recently, minimal linear codes have been extensively studied due to their applications in secret sharing schemes, secure two-party computations, and so on. Constructing minimal linear codes violating the Ashikhmin-Barg condition and then determining their weight distributions have been interesting in coding theory and cryptography. In this paper, a generic construction for ternary linear codes with dimension $m+2$ is presented, where $m$ is an integer, and a necessary and sufficient condition for this ternary linear code to be minimal is derived. Based on this condition and exponential sums, a new class of minimal ternary linear codes violating the Ashikhmin-Barg condition are obtained, and then their complete weight enumerators are determined.