Related papers: A linear programming bound for sum-rank metric cod…

We present an algorithm for the classification of linear codes over finite fields, based on lattice point enumeration. We validate a correct implementation of our algorithm with known classification results from the literature, which we…

Locally repairable codes which are optimal with respect to the bound presented by Prakash et al. are considered. New upper bounds on the length of such optimal codes are derived. The new bounds both improve and generalize previously known…

The tensor product of one code endowed with the Hamming metric and one endowed with the rank metric is analyzed. This gives a code which naturally inherits the sum-rank metric. Specializing to the product of a cyclic code and a skew-cyclic…

We present exact mixed-integer linear programming formulations for verifying the performance of first-order methods for parametric quadratic optimization. We formulate the verification problem as a mixed-integer linear program where the…

We develop a point of view on reduction of multiplicative proof nets based on quantum error-correcting codes. To each proof net we associate a code, in such a way that cut-elimination corresponds to error correction.

We propose new optimal estimators for the Lipschitz frontier of a set of points. They are defined as kernel estimators being sufficiently regular, covering all the points and whose associated support is of smallest surface. The estimators…

The author studies the Cram\'{e}r-Rao type bound by a linear programming approach. By this approach, he found a necessary and sufficient condition that the Cram\'{e}r-Rao type bound is attained by a random measurement. In a spin 1/2 system,…

We introduce two notions of discrepancy between binary vectors, which are not metric functions in general but nonetheless capture the mathematical structure of the binary asymmetric channel. In turn, these lead to two new fundamental…

In this paper, we propose a metric on the space of finite sets of trajectories for assessing multi-target tracking algorithms in a mathematically sound way. The main use of the metric is to compare estimates of trajectories from different…

We propose the first non-trivial generic decoding algorithm for codes in the sum-rank metric. The new method combines ideas of well-known generic decoders in the Hamming and rank metric. For the same code parameters and number of errors,…

We propose a randomized method for solving linear programs with a large number of columns but a relatively small number of constraints. Since enumerating all the columns is usually unrealistic, such linear programs are commonly solved by…

Locally repairable codes (LRCs) are error correcting codes used in distributed data storage. Besides a global level, they enable errors to be corrected locally, reducing the need for communication between storage nodes. There is a close…

The column Hamming distance of a convolutional code determines the error correction capability when streaming over a class of packet erasure channels. We introduce a metric known as the column sum rank, that parallels column Hamming…

With the decline of Moore's law, optimizing program performance has become a major focus of software research. However, high-level optimizations such as API and algorithm changes remain elusive due to the difficulty of understanding the…

Constant dimension codes are used for error control in random linear network coding, so that constructions for these codes with large cardinality have achieved wide attention in the last decade. Here, we improve the so-called linkage…

We consider network coding for networks experiencing worst-case bit-flip errors, and argue that this is a reasonable model for highly dynamic wireless network transmissions. We demonstrate that in this setup prior network error-correcting…

We give one more proof of the first linear programming bound for binary codes, following the line of work initiated by Friedman and Tillich. The new argument is somewhat similar to previous proofs, but we believe it to be both simpler and…

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…

Ternary channels can be used to model the behavior of some memory devices, where information is stored in three different levels. In this paper, error correcting coding for a ternary channel where some of the error transitions are not…

We settle the computational complexity of fundamental questions related to multicriteria integer linear programs, when the dimensions of the strategy space and of the outcome space are considered fixed constants. In particular we construct:…