Affiliation:
1. Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia
2. Department of Mathematics, Dr. Babasaheb Ambedkar Marathwada University, Aurangabad 431004, India
Abstract
Let u,v, and w be indeterminates over Fpm and let R=Fpm+uFpm+vFpm+wFpm, where p is a prime. Then, R is a ring of order p4m, and R≅Fpm[u,v,w]I with maximal ideal J=uFpm+vFpm+wFpm of order p3m and a residue field Fpm of order pm, where I is an appropriate ideal. In this article, the goal is to improve the understanding of linear codes over local non-chain rings. In particular, we investigate the symmetrized weight enumerators and generator matrices of linear codes of length N over R. In order to accomplish that, we first list all such rings up to the isomorphism for different values of the index of nilpotency l of J, 2≤l≤4. Furthermore, we fully describe the lattice of ideals of R and their orders. Next, for linear codes C over R, we compute the generator matrices and symmetrized weight enumerators, as shown by numerical examples.
Funder
King Saud University, Riyadh, Saudi Arabia
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