Zobrazeno 1 - 10
of 334 049
pro vyhledávání: '"REED, P. A."'
Autor:
Con, Roni
In this work, we study the performance of Reed-Solomon codes against an adversary that first permutes the symbols of the codeword and then performs insertions and deletions. This adversarial model is motivated by the recent interest in fully anonymou
Externí odkaz:
http://arxiv.org/abs/2412.17003
Twisted generalized Reed-Solomon (TGRS) codes constitute an interesting family of evaluation codes, containing a large class of maximum distance separable codes non-equivalent to generalized Reed-Solomon (GRS) ones. Moreover, the Schur squares of TGR
Externí odkaz:
http://arxiv.org/abs/2412.15160
Generalized Reed-Solomon codes form the most prominent class of maximum distance separable (MDS) codes, codes that are optimal in the sense that their minimum distance cannot be improved for a given length and code size. The study of codes that are M
Externí odkaz:
http://arxiv.org/abs/2412.08391
Autor:
Hörmann, Felicitas, Bartz, Hannes
Linearized Reed--Solomon (LRS) codes are sum-rank-metric codes that generalize both Reed--Solomon and Gabidulin codes. We study vertically and horizontally interleaved LRS (VILRS and HILRS) codes whose codewords consist of a fixed number of stacked o
Externí odkaz:
http://arxiv.org/abs/2411.19101
MDS codes have garnered significant attention due to their wide applications in practice. To date, most known MDS codes are equivalent to Reed-Solomon codes. The construction of non-Reed-Solomon (non-RS) type MDS codes has emerged as an intriguing an
Externí odkaz:
http://arxiv.org/abs/2411.14779
Autor:
Rameshwar, V. Arvind, Lalitha, V.
In this paper, we revisit the Recursive Projection-Aggregation (RPA) decoder, of Ye and Abbe (2020), for Reed-Muller (RM) codes. Our main contribution is an explicit upper bound on the probability of incorrect decoding, using the RPA decoder, over a
Externí odkaz:
http://arxiv.org/abs/2412.08129
In 1948, Shannon used a probabilistic argument to show the existence of codes achieving a maximal rate defined by the channel capacity. In 1954, Muller and Reed introduced a simple deterministic code construction, based on polynomial evaluations, con
Externí odkaz:
http://arxiv.org/abs/2411.13493
Autor:
Srivastava, Shashank
Folded Reed-Solomon (FRS) codes are variants of Reed-Solomon codes, known for their optimal list decoding radius. We show explicit FRS codes with rate $R$ that can be list decoded up to radius $1-R-\epsilon$ with lists of size $\mathcal{O}(1/ \epsilo
Externí odkaz:
http://arxiv.org/abs/2410.09031
Autor:
Song, Yufeng, Luo, Jinquan
Projective Reed-Muller codes(PRM codes) are constructed from the family of projective hypersurfaces of a fixed degree over a finite field $\F_q$. In this paper, we completely determine the minimal distance of the hull of any Projective Reed-Muller co
Externí odkaz:
http://arxiv.org/abs/2410.07217
Maximum distance separable (MDS) codes have significant combinatorial and cryptographic applications due to their certain optimality. Generalized Reed-Solomon (GRS) codes are the most prominent MDS codes. Twisted generalized Reed-Solomon (TGRS) codes
Externí odkaz:
http://arxiv.org/abs/2408.12049