Our main technical result is that, in the coset leader graph of a linear binary code of block length n, the metric balls spanned by constant-weight vectors grow exponentially slower than those in {0, 1}n . Following the approach of [1], we use this fact to improve on the first linear programming bound on the rate of LDPC codes, as the function of their minimal relative distance. This improvement, combined with the techniques of [2], improves the rate vs distance bounds for LDPC codes in a significant sub-range of relative distances.

If R is an integral domain and K is its field of fractions, we letshow that if R is the ring of integers of a p-adic field, then Int(R) is generated, as an R-algebra, by the coefficients of the endomorphisms of any Lubin-Tate group attached to R.

The challenge of autonomous indoor mapping is addressed. The goal is to minimize the time required to achieve a predefined percentage of coverage with some desired level of certainty. The use of a pre-trained generative deep neural network, acting as a map predictor, in both the motion planning and the map construction is proposed in order to expedite the mapping process. The issue of planning under partial observability is tackled by maintaining a belief map of the floorplan, generated by a deep neural network. This allows the agent to shorten the mapping duration, as well as enabling it to make better-informed decisions. This method is examined in combination with several motion planners for two distinct floorplan datasets. Simulations are run for several configurations of the integrated map predictor, the results of which reveal that by utilizing the prediction a significant reduction in mapping time is possible. When the prediction is integrated in both motion planning and map construction processes it is shown that the mapping time may in some cases be cut by over 50%.

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We suggest a new approach to obtain bounds on locally correctable and some locally testable binary linear codes, by arguing that these codes (or their subcodes) have coset leader graphs with high discrete Ricci curvature.The bounds we obtain for locally correctable codes are worse than the best known bounds obtained using quantum information theory, but are better than those obtained using other methods, such as the "usual" information theory. (We remark that our methods are completely elementary.)The bounds we obtain for a family of locally testable codes improve the best known bounds.