Related papers: A New Construction of Non-Binary Deletion Correcti…
One peculiarity with deletion-correcting codes is that perfect $t$-deletion-correcting codes of the same length over the same alphabet can have different numbers of codewords, because the balls of radius $t$ with respect to the…
We construct an explicit family of locally repairable and locally regenerating codes whose existence was proven in a recent work by Kamath et al. about codes with local regeneration but no explicit construction was given. This explicit…
Reed-Solomon (RS) codes are an important class of non-binary error-correction codes. They are particularly competent in correcting burst errors, being widely applied in modern communications and data storage systems. This also thanks to…
We present the construction of a new family of erasure correcting codes for distributed storage that yield low repair bandwidth and low repair complexity. The construction is based on two classes of parity symbols. The primary goal of the…
We give a complete answer to the following basic question: "What is the maximal fraction of deletions or insertions tolerable by $q$-ary list-decodable codes with non-vanishing information rate?" This question has been open even for binary…
Motivated by DNA-based storage applications, we study the problem of reconstructing a coded sequence from multiple traces. We consider the model where the traces are outputs of independent deletion channels, where each channel deletes each…
In this paper, we discuss a construction method of quantum deletion error-correcting codes. First of all, we define deletion errors for quantum states, an encoder, a decoder, and two conditions which is expressed by only the combinatorial…
In recent years, the emergence of DNA storage systems has led to a widespread focus on the research of codes correcting insertions, deletions, and classic substitutions. During the initial investigation, Levenshtein discovered the VT codes…
An alternative permutation decoding method is described which can be used for any binary systematic encoding scheme, regardless whether the code is linear or not. Thus, the method can be applied to some important codes such as Z2Z4-linear…
Boolean functions have very nice applications in cryptography and coding theory, which have led to a lot of research focusing on their applications. The objective of this paper is to construct binary linear codes with few weights from the…
We address the maximum size of binary codes and binary constant weight codes with few distances. Previous works established a number of bounds for these quantities as well as the exact values for a range of small code lengths. As our main…
Reconstruction codes are generalizations of error-correcting codes that can correct errors by a given number of noisy reads. The study of such codes was initiated by Levenshtein in 2001 and developed recently due to applications in modern…
Binary code analysis has immense importance in the research domain of software security. Today, software is very often compiled for various Instruction Set Architectures (ISAs). As a result, cross-architecture binary code analysis has…
Guess & Check (GC) codes are systematic binary codes that can correct multiple deletions, with high probability. GC codes have logarithmic redundancy in the length of the message $k$, and the encoding and decoding algorithms of these codes…
Much work has been done to identify which binary codes can be represented by collections of open convex or closed convex sets. While not all binary codes can be realized by such sets, here we prove that every binary code can be realized by…
In order to provide high data reliability, distributed storage systems disperse data with redundancy to multiple storage nodes. Regenerating codes is a new class of erasure codes to introduce redundancy for the purpose of improving the data…
In this paper we describe a variation of the classical permutation decoding algorithm that can be applied to any affine-invariant code with respect to certain type of information sets. In particular, we can apply it to the family of…
All codes with minimum distance 8 and codimension up to 14 and all codes with minimum distance 10 and codimension up to 18 are classified. Nonexistence of codes with parameters [33,18,8] and [33,14,10] is proved. This leads to 8 new exact…
We investigate the packing and covering densities of linear and nonlinear binary codes, and establish a number of duality relationships between the packing and covering problems. Specifically, we prove that if almost all codes (in the class…
We present a novel technique for encoding and decoding constant weight binary codes that uses a geometric interpretation of the codebook. Our technique is based on embedding the codebook in a Euclidean space of dimension equal to the weight…