2021/07/16 by Guruswami, Venkatesan, Riazanov, Andrii
#FOS: Computer and information sciences #Information Theory (cs.IT)
paper · doi:10.48550/arxiv.2107.07672
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 optimal solution to Delsarte's LP for the almost-balanced case with large distance d ≥ (n - √(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.