AntiGriesmer Bounds, Optimal Codes, and Their Subcode Support Weight Distributions
Abstract
In this paper, we present an antiGriesmer lower bound on the subcode support weights of projective linear codes. This bound is a lower bound on the maximumr-dimensional subcode support weights of projective linear codes. Based on the r-dimensional subcode support weight distributions (r-SSWDs) of linear codes, we compute ther-SSWDs for their simplex complementary codes. Then we construct several infinite families of distance-optimal codes meeting the ℓ-generalized Hamming weight Griesmer bound. These codes do not achieve the Griesmer bound for thej-generalized Hamming weight, where 1 ≤j< ℓ. Moreover, subcode support weight distributions of these optimal linear codes are determined.
Fields of Study & Subjects
Coding theory and cryptography
Error Correcting Code Techniques
Advanced Combinatorial Mathematics
Publication details
- Journal / source
- IEEE Transactions on Information Theory
- Volume
- 72
- Issue
- 4
- Pages
- 2133–2143
- Publication date
- 17 February 2026
- Language
- EN