Linear programming bounds for binary and ternary LCD Codes

@misc{kang2026linear,
  title = {{Linear programming bounds for binary and ternary LCD Codes}},
  author = {Ming-Hsuan Kang and Maosheng Xiong},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.08662},
  eprint = {2609.08662},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.08662},
}

TY  - UNPB
TI  - Linear programming bounds for binary and ternary LCD Codes
AU  - Ming-Hsuan Kang
AU  - Maosheng Xiong
PY  - 2026
DA  - 2026/09/14
PB  - arXiv
DO  - 10.48550/arxiv.2609.08662
UR  - https://arxiv.org/abs/2609.08662
AB  - We derive linear programming (LP) bounds on the minimum distance of binary and ternary linear complementary dual (LCD) codes by imposing arithmetic constraints on their weight enumerators. Special values of the weight enumerator give finitely many Gauss phases, each of which yields linear equations in the ordinary weight-distribution variables. The resulting bounds strengthen the real-valued LCD counting LP without introducing additional variables; both the number of branches and the number of added equations per branch are bounded independently of the code length. Exact certificates establish strict improvements for 62 binary parameter pairs of length at most 20 and 39 ternary pairs of length at most 14. For four binary pairs, the bounds also improve the joint-weight-enumerator LP while using fewer variables per branch. These comparisons show that Gauss-phase information provides a compact strengthening of existing LP relaxations for LCD codes.
ER  -