2025/04/17 by Zhiyong Zheng, Fengxia Liu, Zheng, Zhiyong +3
Computer Science · Mathematics · Engineering · #Coding theory and cryptography #Finite Group Theory Research #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.2504.12604
In this paper, we study linear codes over ℤk based on lattices and theta functions. We obtain the complete weight enumerators MacWilliams identity and the symmetrized weight enumerators MacWilliams identity based on the theory of theta function. We extend the main work by Bannai, Dougherty, Harada and Oura to the finite ring ℤk for any positive integer k and present the complete weight enumerators MacWilliams identity in genus g. When k=p is a prime number, we establish the relationship between the theta function of associated lattices over a cyclotomic field and the complete weight enumerators with Hamming weight of codes, which is an analogy of the results by G. Van der Geer and F. Hirzebruch since they showed the identity with the Lee weight enumerators.