2025/12/16 by Xiumei Li, Li, Xiumei, Xiaotong Sun +3
Computer Science · Mathematics · Engineering · #Coding theory and cryptography #Finite Group Theory Research #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.2512.14073
In this paper, for an odd prime power q, we extend the construction of Xie et al. \citeXOYM2023 to propose two classes of linear codes CQ and CQ' over the finite field \mathbbFq with at most four nonzero weights. These codes are derived from quadratic forms through a bivariate construction. We completely determine their complete weight enumerators and weight hierarchies by employing exponential sums. Most of these codes are minimal and some are optimal in the sense that they meet the Griesmer bound. Furthermore, we also establish the weight hierarchies of CQ,N and CQ,N', which are the descended codes of CQ and CQ'.