Related papers: Status of the MARS code
The matrix completion problem provides a unifying lens through which many fundamental problems in coding theory can be viewed. In this paper, we investigate Locally Recoverable Codes (LRCs) with Maximal Recoverability (MR) and Maximum…
In this work, we provide four methods for constructing new maximum sum-rank distance (MSRD) codes. The first method, a variant of cartesian products, allows faster decoding than known MSRD codes of the same parameters. The other three…
This paper outlines image domain material decomposition algorithms that have been routinely used in MARS spectral CT systems. These algorithms (known collectively as MARS-MD) are based on a pragmatic heuristic for solving the…
We investigate two classes of extended codes and provide necessary and sufficient conditions for these codes to be non-GRS MDS codes. We also determine the parity check matrices for these codes. Using the connection of MDS codes with arcs…
Maximum Distance Separable (MDS) codes with a sparse and balanced generator matrix are appealing in distributed storage systems for balancing and minimizing the computational load. Such codes have been constructed via Reed-Solomon codes…
Comprehensive evaluation of machine learning models is the key to make sure that they perform as robustly and consistently as desired. In order to summarize the experimental results and pick a winner, Critical Difference (CD) diagrams are…
Advancements in LLMs have enhanced task automation in software engineering; however, current evaluations primarily focus on natural language tasks, overlooking code quality. Most benchmarks prioritize high-level reasoning over executable…
Maximum distance separable (MDS) and near maximum distance separable (NMDS) codes have been widely used in various fields such as communication systems, data storage, and quantum codes due to their algebraic properties and excellent…
Self-dual maximum distance separable codes (self-dual MDS codes) and self-dual near MDS codes are very important in coding theory and practice. Thus, it is interesting to construct self-dual MDS or self-dual near MDS codes. In this paper,…
It is an important task to construct quantum maximum-distance-separable (MDS) codes with good parameters. In the present paper, we provide six new classes of q-ary quantum MDS codes by using generalized Reed-Solomon (GRS) codes and…
Numerical methods have become a powerful tool for research in astrophysics, but their utility depends critically on the availability of suitable simulation codes. This calls for continuous efforts in code development, which is necessitated…
Rank-metric codes, defined as sets of matrices over a finite field with the rank distance, have gained significant attention due to their applications in network coding and connections to diverse mathematical areas. Initially studied by…
Electronic structure simulation (ESS) has been used for decades to provide quantitative scientific insights on an atomistic scale, enabling advances in chemistry, biology, and materials science, among other disciplines. Following standard…
Lifted maximum rank distance (MRD) codes, which are constant dimension codes, are considered. It is shown that a lifted MRD code can be represented in such a way that it forms a block design known as a transversal design. A slightly…
Codec-based text-to-speech (TTS) models have shown impressive quality with zero-shot voice cloning abilities. However, they often struggle with more expressive references or complex text inputs. We present MARS6, a robust encoder-decoder…
Code LLMs have become extremely popular recently for modeling source code across a variety of tasks, such as generation, translation, and summarization. However, transformer-based models are limited in their capabilities to reason through…
Given any linear code $C$ over a finite field $GF(q)$ we show how $C$ can be described in a transparent and geometrical way by using the associated Bruen-Silverman code. Then, specializing to the case of MDS codes we use our new approach to…
This preprint is of a chapter to appear in {\it Combinatorics and finite fields: Difference sets, polynomials, pseudorandomness and applications. Radon Series on Computational and Applied Mathematics}, K.-U. Schmidt and A. Winterhof (eds.).…
One to Many communications are expected to be among the killer applications for the currently discussed 5G standard. The usage of coding mechanisms is impacting broadcasting standard quality, as coding is involved at several levels of the…
Few Shot Segmentation aims to segment novel object classes given only a handful of labeled examples, enabling rapid adaptation with minimal supervision. Current literature crucially lacks a selection method that goes beyond visual…