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The matrix representations of linear codes have been well-studied for use as disjunct matrices. However, no connection has previously been made between the properties of disjunct matrices and the parity-check codes obtained from them. This…
Reliability is an important requirement for both communication and storage systems. Due to continuous scale down of technology multiple adjacent bits error probability increases. The data may be corrupted due soft errors. Error correction…
The ability to store data in the DNA of a living organism has applications in a variety of areas including synthetic biology and watermarking of patented genetically-modified organisms. Data stored in this medium is subject to errors…
Defects4J has enabled numerous software testing and debugging research work since its introduction. A large part of its contribution, and the resulting popularity, lies in the clear separation and distillation of the root cause of each…
In order to achieve fault tolerance, highly reliable system often require the ability to detect errors as soon as they occur and prevent the speared of erroneous information throughout the system. Thus, the need for codes capable of…
In Index coding there is a single sender with multiple messages and multiple receivers each wanting a different set of messages and knowing a different set of messages a priori. The Index Coding problem is to identify the minimum number of…
A problem of index coding with side information was first considered by Y. Birk and T. Kol (IEEE INFOCOM, 1998). In the present work, a generalization of index coding scheme, where transmitted symbols are subject to errors, is studied.…
We consider the problem of block-coded communication, where in each block, the channel law belongs to one of two disjoint sets. The decoder is aimed to decode only messages that have undergone a channel from one of the sets, and thus has to…
Tandem duplication in DNA is the process of inserting a copy of a segment of DNA adjacent to the original position. Motivated by applications that store data in living organisms, Jain {\em et al.} (2016) proposed the study of codes that…
The code that combines channel estimation and error protection has received general attention recently, and has been considered a promising methodology to compensate multi-path fading effect. It has been shown by simulations that such code…
Separable codes were introduced to provide protection against illegal redistribution of copyrighted multimedia material. Let $\mathcal{C}$ be a code of length $n$ over an alphabet of $q$ letters. The descendant code ${\sf…
The color code is a topological quantum error-correcting code supporting a variety of valuable fault-tolerant logical gates. Its two-dimensional version, the triangular color code, may soon be realized with currently available…
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 consider the recently introduced concept of \emph{function-correcting codes (FCCs) with data protection}, which provide a certain level of error protection for the data and a higher level of protection for a desired…
The first linear code supporting a $4$-design was the $[11, 6, 5]$ ternary Golay code discovered in 1949 by Golay. In the past 71 years, sporadic linear codes holding $4$-designs or $5$-designs were discovered and many infinite families of…
Cyclic codes are an important subclass of linear codes with wide applications in communication systems and data storage systems. In 2013, Ding and Helleseth presented nine open problems on optimal ternary cyclic codes $\mathcal{C}_{(1,e)}$.…
In this work we investigate codes in $\mathbb{Z}_{2^m}^n$ that can correct errors that occur in just one coordinate of the codeword, with a magnitude of up to a given parameter $t$. We will show upper bounds on these cross codes, derive…
A problem of index coding with side information was first considered by Y. Birk and T. Kol (IEEE INFOCOM, 1998). In the present work, a generalization of index coding scheme, where transmitted symbols are subject to errors, is studied.…
In this paper, we present error-correcting codes which are the results of our research on the sub-exceeding functions. For a short and medium distance data transmission (wifi network, bluetooth, cable, ...), we see that these codes…
We establish a construction of optimal authentication codes achieving perfect multi-fold secrecy by means of combinatorial designs. This continues the author's work (ISIT 2009) and answers an open question posed therein. As an application,…