Related papers: Errata list for "Error Control Coding" by Lin and …
We prove the following results concerning the list decoding of error-correcting codes: (i) We show that for \textit{any} code with a relative distance of $\delta$ (over a large enough alphabet), the following result holds for \textit{random…
This chapter is written for the forthcoming book "A Concise Encyclopedia of Coding Theory" (CRC press), edited by W. Cary Huffman, Jon-Lark Kim, and Patrick Sol\'e. This book will collect short but foundational articles, emphasizing…
This paper gives some theory and efficient design of binary block systematic codes capable of controlling the deletions of the symbol ``$0$'' (referred to as $0$-deletions) and/or the insertions of the symbol ``$0$'' (referred to as…
Upper and lower bounds are given for the number of equivalence classes of error patterns in the toric code for quantum memory. The results are used to derive a lower bound on the ground-state energy of the +/-J Ising spin glass model on the…
We construct error correcting codes for jointly transmitting a finite set of independent messages to an 'informed receiver' which has prior knowledge of the values of some subset of the messages as side information. The transmitter is…
In this paper, we study binary constrained codes that are resilient to bit-flip errors and erasures. In our first approach, we compute the sizes of constrained subcodes of linear codes. Since there exist well-known linear codes that achieve…
In this paper, new index coding problems are studied, where each receiver has erroneous side information. Although side information is a crucial part of index coding, the existence of erroneous side information has not yet been considered.…
The complexity of the error correction circuitry forces us to design quantum error correction codes capable of correcting a single error per error correction cycle. Yet, time-correlated error are common for physical implementations of…
Quantum computers face significant challenges from quantum deviations or coherent noise, particularly during gate operations, which pose a complex threat to the efficacy of quantum error correction (QEC) protocols. In this study, we…
Claims by Kroha and Zawadowski in cond-mat/0105026 on inadequate approximations and an incorrect statement in cond-mat/0102150 are shown to be based on oversimplified estimates and a false quotation.
In this paper, we show that the code-trellis and the error-trellis for a convolutional code can be reduced simultaneously, if reduction is possible. Assume that the error-trellis can be reduced using shifted error-subsequences. In this…
Secure storage of noisy data for authentication purposes usually involves the use of error correcting codes. We propose a new model scenario involving burst errors and present for that several constructions.
After a brief introduction to both quantum computation and quantum error correction, we show how to construct quantum error-correcting codes based on classical BCH codes. With these codes, decoding can exploit additional information about…
Series of maximum distance quantum error-correcting codes are developed and analysed. For a given rate and given error-correction capability, quantum error-correcting codes with these specifications are constructed. The codes are explicit…
Program errors can occur in any type of programming, and can manifest in a variety of ways, such as unexpected output, crashes, or performance issues. And program error diagnosis can often be too abstract or technical for developers to…
Correction to Bernoulli (2006), 12, 551--570 http://projecteuclid.org/euclid.bj/1151525136
Quantum error correction is necessary to perform large-scale quantum computations in the presence of noise and decoherence. As a result, several aspects of quantum error correction have already been explored. These have been primarily…
At ITW'10, Bringer et al. suggest to strengthen their previous identification protocol by extending the Code Reverse Engineering (CRE) problem to identification codes. We first extend security results by Tillich et al. on this very problem.…
This short report raises a correctness issue in the schedulability test presented in Kato et al., "Gang EDF Scheduling of Parallel Task Systems", 30th IEEE Real-Time Systems Symposium, 2009, pp. 459-468.
We present efficient decoding algorithms from square-root errors for two known families of double-circulant codes: A construction based on Sidon sets (Bhargava, Taveres, and Shiva, \emph{IEEE IT 74}; Calderbank, \emph{IEEE IT 83}; Guruswami…