In this paper, several infinite families of codes over the extension of non-unital non-commutative rings are constructed utilizing general simplicial complexes. Thanks to the special structure of the defining sets, the principal parameters of these codes are characterized. Specially, when the employed simplicial complexes are generated by a single maximal element, we determine their Lee weight distributions completely. Furthermore, by considering the Gray image codes and the corresponding subfield-like codes, numerous of linear codes over F-q are also obtained, where q is a prime power. Certain conditions are given to ensure the above linear codes are (Hermitian) self-orthogonal in the case of q=2,3,4 . It is noteworthy that most of the derived codes over F-q satisfy the Ashikhmin-Barg's condition for minimality. Besides, we obtain two infinite families of distance-optimal codes over F(q )with respect to the Griesmer bound. By puncturing the Gray image codes and subfield-like codes, several classes of projective codes are presented.

Publication:

IEEE TRANSACTIONS ON INFORMATION THEORY

http://dx.doi.org/10.1109/TIT.2026.3669473

Author:

Yanan Wu

the School of Mathematical Sciences and the Key Laboratory of Pure Mathematics and Combinatorics (LPMC), Nankai University, Tianjin 300100, China

e-mail: yanan.wu@aliyun.com

Tingting Pang

the School of Information Science and Engineering, Shandong Normal University, Jinan 250358, China

e-mail: pangtingting@sdnu.edu.cn

Nian Li

the Key Laboratory of Intelligent Sensing System and Security, Ministry of Education, Hubei Provincial Engineering Research Center of Intelligent Connected Vehicle Network Security, and the School of Cyber Science and Technology, Hubei University, Wuhan 430062, China

Corresponding author

e-mail: nian.li@hubu.edu.cn

Yanbin Pan

the Key Laboratory of Mathematics Mechanization, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China

e-mail: panyanbin@amss.ac.cn

Xiangyong Zeng

the Key Laboratory of Intelligent Sensing System and Security, Ministry of Education, Hubei Key Laboratory of Applied Mathematics, and the Faculty of Mathematics and Statistics, Hubei University, Wuhan 430062, China

e-mail: xiangyongzeng@aliyun.com