Related papers: On Function-Correcting Codes in the Lee Metric
The Gilbert type bound for codes in the title is reviewed, both for small and large alphabets. Constructive lower bounds better than these existential bounds are derived from geometric codes, either over Fp or Fp2 ; or over even degree…
The family of functions plays a central role in the design and effectiveness of function-correcting codes. By focusing on a well-defined family of functions, function-correcting codes can be constructed with minimal length while still…
Linear codes play a central role in coding theory and have applications in several branches of mathematics. For error correction purposes the minimum Hamming distance should be as large as possible. Linear codes related to applications in…
We introduce function-correcting partition codes (FCPCs), which are a natural generalization of function-correcting codes (FCCs). An FCPC is defined directly on a partition of the message space, rather than on a specific target function. We…
Currently known secondary construction techniques for linear codes mainly include puncturing, shortening, and extending. In this paper, we propose a novel method for the secondary construction of linear codes based on their weight…
This paper examines linear binary codes capable of correcting one or more errors. For the single-error-correcting case, it is shown that the Hamming bound is achieved by a constructive method, and an exact expression for the minimal…
Sum-rank Hamming codes are introduced in this work. They are essentially defined as the longest codes (thus of highest information rate) with minimum sum-rank distance at least $ 3 $ (thus one-error-correcting) for a fixed redundancy $ r $,…
Consider a binary word being transmitted through a communication channel that introduces deletable errors where each bit of the word is either retained, flipped, erased or deleted. The simplest code for correcting \emph{all} possible…
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…
A covering code is a set of codewords with the property that the union of balls, suitably defined, around these codewords covers an entire space. Generally, the goal is to find the covering code with the minimum size codebook. While most…
Locally repairable codes (LRCs) are error correcting codes used in distributed data storage. Besides a global level, they enable errors to be corrected locally, reducing the need for communication between storage nodes. There is a close…
We examine an error-correcting coding framework in which each coded symbol is constrained to be a function of a fixed subset of the message symbols. With an eye toward distributed storage applications, we seek to design systematic codes…
Function-correcting codes with data protection simultaneously protect both the data and a function of the data at distinct error-correction levels. When the function receives strictly stronger protection than the data, such a code is called…
Most low-density parity-check (LDPC) code constructions are considered over finite fields. In this work, we focus on regular LDPC codes over integer residue rings and analyze their performance with respect to the Lee metric. Their…
In this thesis we present several results in coding theory, concerning error-correcting codes and the Shannon capacity. 1. We give a general symmetry reduction of matrices occuring in semidefinite programs in coding theory. 2. We apply the…
Based on the theoretical neuroscience, G. Cotardo and A. Ravagnavi in \cite{CR} introduced a kind of asymmetric binary codes called combinatorial neural codes (CN codes for short), with a "matched metric" $\delta_{r}$ called asymmetric…
This work investigates the structure of rank-metric codes in connection with concepts from finite geometry, most notably the $q$-analogues of projective systems and blocking sets. We also illustrate how to associate a classical…
As a medium for cold data storage, DNA stands out as it promises significant gains in storage capacity and lifetime. However, it comes with its own data processing challenges to overcome. Constrained codes over the DNA alphabet…
This paper studies the cardinality of codes correcting insertions and deletions. We give improved upper and lower bounds on code size. Our upper bound is obtained by utilizing the asymmetric property of list decoding for insertions and…
We consider network coding for networks experiencing worst-case bit-flip errors, and argue that this is a reasonable model for highly dynamic wireless network transmissions. We demonstrate that in this setup prior network error-correcting…