8 papers
On the Generalized Packing and Covering Radii of Codes
Wenjun Yu, Moshe Schwartz
The minimum distance and the covering radius are two fundamental properties of the code. Both have been extended: the former to the generalized Hamming weights hierarchy, and the l…
On the Capacity of Sequences of Coloring Channels
Wenjun Yu, Moshe Schwartz
A single coloring channel is defined by a subset of letters it allows to pass through, while deleting all others. A sequence of coloring channels provides multiple views of the sam…
Optimal Reconstruction Codes with Given Reads in Multiple Burst-Substitutions Channels
Wenjun Yu, Yubo Sun, Zixiang Xu +2
We study optimal reconstruction codes over the multiple-burst substitution channel. Our main contribution is establishing a trade-off between the error-correction capability of the…
On Zero Skip-Cost Generalized Fractional-Repetition Codes from Covering Designs
Wenjun Yu, Bo-Jun Yuan, Moshe Schwartz
We study generalized fractional repetition codes that have zero skip cost, and which are based on covering designs. We show that a zero skip cost is always attainable, perhaps at a…
The Second Generalized Covering Radius of Binary Primitive Double-Error-Correcting BCH Codes
Lev Yohananov, Moshe Schwartz
We completely determine the second covering radius for binary primitive double-error-correcting BCH codes. As part of this process, we provide a lower bound on the second covering…
On the Asymptotic Rate of Optimal Codes that Correct Tandem Duplications for Nanopore Sequencing
Wenjun Yu, Zuo Ye, Moshe Schwartz
We study codes that can correct backtracking errors during nanopore sequencing. In this channel, a sequence of length over an alphabet of size is being read by a sliding wi…
On Duplication-Free Codes for Disjoint or Equal-Length Errors
Wenjun Yu, Moshe Schwartz
Motivated by applications in DNA storage, we study a setting in which strings are affected by tandem-duplication errors. In particular, we look at two settings: disjoint tandem-dup…
On the Coding Capacity of Reverse-Complement and Palindromic Duplication-Correcting Codes
Lev Yohananov, Moshe Schwartz
We derive the coding capacity for duplication-correcting codes capable of correcting any number of duplications. We do so both for reverse-complement duplications, as well as palin…