Zobrazeno 1 - 10
of 141 346
pro vyhledávání: '"P, Solomon"'
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:
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
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
Autor:
Bajaj, Bhavuk Sikka
This study addresses the use of Reed-Solomon error correction codes in QR codes to enhance resilience against failures. To fully grasp this approach, a basic cryptographic context is provided, necessary for understanding Reed-Solomon codes. The study
Externí odkaz:
http://arxiv.org/abs/2407.17364
In this paper, we prove that with high probability, random Reed-Solomon codes approach the half-Singleton bound - the optimal rate versus error tradeoff for linear insdel codes - with linear-sized alphabets. More precisely, we prove that, for any $\e
Externí odkaz:
http://arxiv.org/abs/2407.07299
Autor:
Chen, Yeyuan, Zhang, Zihan
In this paper, we prove that explicit FRS codes and multiplicity codes achieve relaxed generalized Singleton bounds for list size $L\ge1.$ Specifically, we show the following: (1) FRS code of length $n$ and rate $R$ over the alphabet $\mathbb{F}_q^s$
Externí odkaz:
http://arxiv.org/abs/2408.15925
Autor:
Chen, Hao
In their fundamental paper published in 1965, G. Solomon and J. J. Stiffler invented infinite families of codes meeting the Griesmer bound. These codes are then called Solomon-Stiffler codes and have motivated various constructions of codes meeting o
Externí odkaz:
http://arxiv.org/abs/2406.10825
Autor:
Dinh, Thi Xinh, Le, Ba Thong, Dau, Son Hoang, Boztas, Serdar, Kruglik, Stanislav, Kiah, Han Mao, Viterbo, Emanuele, Etzion, Tuvi, Chee, Yeow Meng
We generalize the problem of recovering a lost/erased symbol in a Reed-Solomon code to the scenario in which some side information about the lost symbol is known. The side information is represented as a set $S$ of linearly independent combinations o
Externí odkaz:
http://arxiv.org/abs/2405.07180
We investigate the problem of privately recovering a single erasure for Reed-Solomon codes with low communication bandwidths. For an $[n,k]_{q^\ell}$ code with $n-k\geq q^{m}+t-1$, we construct a repair scheme that allows a client to recover an arbit
Externí odkaz:
http://arxiv.org/abs/2405.06583