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Paper IDD3-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.