| Paper ID | D3-S5-T2.3 |
| Paper Title |
Linear Programming Bounds for Almost-Balanced Binary Codes |
| Authors |
Venkatesan Guruswami, Andrii Riazanov, Carnegie Mellon University, United States |
| Session |
D3-S5-T2: Topics in Coding II |
| Chaired Session: |
Wednesday, 14 July, 23:20 - 23:40 |
| Engagement Session: |
Wednesday, 14 July, 23:40 - 00:00 |
| Abstract |
We revisit the linear programming bounds for the size vs. distance trade-off for binary codes, focusing on the bounds for the almost-balanced case, when all pairwise distances are between $d$ and $n-d$, where $d$ is the code distance and $n$ is the block length. We give an \emph{optimal} solution to Delsarte's LP for the almost-balanced case with large distance $d \geq (n - \sqrt{n})/2 + 1$, which shows that the optimal value of the LP coincides with the Grey-Rankin bound for self-complementary codes. We also show that a limitation of the asymptotic LP bound shown by Samorodnitsky, namely that it is at least the average of the first MRRW upper bound and Gilbert-Varshamov bound, continues to hold for the almost-balanced case.
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