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pro vyhledávání: '"Jany, Benjamin"'
Autor:
Jany, Benjamin, Ravagnani, Alberto
We investigate the maximum cardinality and the mathematical structure of error-correcting codes endowed with the Kendall-$\tau$ metric. We establish an averaging bound for the cardinality of a code with prescribed minimum distance, discuss its sharpn
Externí odkaz:
http://arxiv.org/abs/2405.14228
We develop a duality theory of locally recoverable codes (LRCs) and apply it to establish a series of new bounds on their parameters. We introduce and study a refined notion of weight distribution that captures the code's locality. Using a duality re
Externí odkaz:
http://arxiv.org/abs/2309.03676
We study the direct sum of q-matroids by way of their cyclic flats. Using that the rank function of a q-matroid is fully determined by the cyclic flats and their ranks, we show that the cyclic flats of the direct sum of two q-matroids are exactly all
Externí odkaz:
http://arxiv.org/abs/2302.02260
We initiate the study of the duality theory of locally recoverable codes, with a focus on the applications. We characterize the locality of a code in terms of the dual code, and introduce a class of invariants that refine the classical weight distrib
Externí odkaz:
http://arxiv.org/abs/2212.07805
While there are many parallels between matroid theory and $q$-matroid theory, most notably on the level of cryptomorphisms, there are substantial differences when it comes to the direct sum. The direct sum of $q$-matroids has been introduced in the l
Externí odkaz:
http://arxiv.org/abs/2211.11626
Autor:
Jany, Benjamin
In this paper, we investigate the relation between a $q$-matroid and its associated matroid called the projectivization matroid. The latter arises by projectivizing the groundspace of the $q$-matroid and considering the projective space as the ground
Externí odkaz:
http://arxiv.org/abs/2204.01232
q-Matroids form the q-analogue of classical matroids. In this paper we introduce various types of maps between q-matroids. These maps are not necessarily linear, but they map subspaces to subspaces and respect the q-matroid structure in certain ways.
Externí odkaz:
http://arxiv.org/abs/2111.09723
This paper is devoted to the study of independent spaces of q-polymatroids. With the aid of an auxiliary q-matroid it is shown that the collection of independent spaces satisfies the same properties as for q-matroids. However, in contrast to q-matroi
Externí odkaz:
http://arxiv.org/abs/2105.01802
It is well known that linear rank-metric codes give rise to q-polymatroids. Analogously to matroid theory one may ask whether a given q-polymatroid is representable by a rank-metric code. We provide an answer by presenting an example of a q-matroid t
Externí odkaz:
http://arxiv.org/abs/2104.06570
Publikováno v:
In European Journal of Combinatorics August 2023 112