Zobrazeno 1 - 10
of 79
pro vyhledávání: '"Weger, Violetta"'
Famous results state that the classical MacWilliams identities fail for the Lee metric, the homogeneous metric and for the subfield metric, apart from some trivial cases. In this paper we change the classical idea of enumerating the codewords of the
Externí odkaz:
http://arxiv.org/abs/2409.11926
Independent parallel q-ary symmetric channels are a suitable transmission model for several applications. The proposed weighted-Hamming metric is tailored to this setting and enables optimal decoding performance. We show that some weighted-Hamming-me
Externí odkaz:
http://arxiv.org/abs/2401.17801
Autor:
Bariffi, Jessica, Weger, Violetta
This paper provides new and improved Singleton-like bounds for Lee metric codes over integer residue rings. We derive the bounds using various novel definitions of generalized Lee weights based on different notions of a support of a linear code. In t
Externí odkaz:
http://arxiv.org/abs/2307.06079
We consider $t$-Lee-error-correcting codes of length $n$ over the residue ring $\mathbb{Z}_m := \mathbb{Z}/m\mathbb{Z}$ and determine upper and lower bounds on the number of $t$-Lee-error-correcting codes. We use two different methods, namely estimat
Externí odkaz:
http://arxiv.org/abs/2305.05763
Autor:
Baldi, Marco, Bitzer, Sebastian, Pavoni, Alessio, Santini, Paolo, Wachter-Zeh, Antonia, Weger, Violetta
Several recently proposed code-based cryptosystems base their security on a slightly generalized version of the classical (syndrome) decoding problem. Namely, in the so-called restricted (syndrome) decoding problem, the error values stem from a restr
Externí odkaz:
http://arxiv.org/abs/2303.08882
We determine the asymptotic proportion of free modules over finite chain rings with good distance properties and treat the asymptotics in the code length n and the residue field size q separately. We then specialize and apply our technique to rank me
Externí odkaz:
http://arxiv.org/abs/2212.09568
Publikováno v:
Journal of Algebra and Its Applications Vol. 23, No. 7 (2024) 2550063
We introduce a new weight and corresponding metric over finite extension fields for asymmetric error correction. The weight distinguishes between elements from the base field and the ones outside of it, which is motivated by asymmetric quantum codes.
Externí odkaz:
http://arxiv.org/abs/2212.00431
Autor:
Porwal, Anmoal, Holzbaur, Lukas, Liu, Hedongliang, Renner, Julian, Wachter-Zeh, Antonia, Weger, Violetta
Due to the recent challenges in post-quantum cryptography, several new approaches for code-based cryptography have been proposed. For example, a variant of the McEliece cryptosystem based on interleaved codes was proposed. In order to deem such new s
Externí odkaz:
http://arxiv.org/abs/2205.14068
The Lee metric syndrome decoding problem is an NP-hard problem and several generic decoders have been proposed. The observation that such decoders come with a larger cost than their Hamming metric counterparts make the Lee metric a promising alternat
Externí odkaz:
http://arxiv.org/abs/2205.12903
In this paper, we study the hardness of decoding a random code endowed with the cover metric. As the cover metric lies in between the Hamming and rank metric, it presents itself as a promising candidate for code-based cryptography. We give a polynomi
Externí odkaz:
http://arxiv.org/abs/2205.12738