# Linear Error Correcting Codes

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### CSE 533: Error-Correcting Codes: Constructions And Algorithms ...

sty for preparing lecture notes. Lecture 1 - A Hat puzzle; Basic definitions about codes; Rate and Distance; Linear codes; [7,4,3] Hamming code ... [ReadMore..]

### Linear-time Encodable And Decodable Error-correcting Codes | IEEE ...

We present a new class of asymptotically good, linear error-correcting codes. These codes can be both encoded and decoded in linear time. They can also be encoded by logarithmic-depth circuits of linear size and decoded by logarithmic depth circuits of size O(nlogn). We present both randomized and explicit constructions of these codes. We present a new class of asymptotically good, linear error-correcting codes. These codes can be both encoded and decoded in linear time. [ReadMore..]

### On Products Of Linear Error Correcting Codes

In this thesis we study products of linear error correcting codes. ... linear code and Hamming distance, which model the copy of M in E contain-. [ReadMore..]

### Error Correcting Codes: A Mathematical Introduction (Chapman Hall ...

Error Correcting Codes: A Mathematical Introduction (Chapman Hall/CRC Mathematics Series) Error Correcting Codes contains not only straight maths, but also exercises on more investigational problem solving. Chapters on number theory and polynomial ... [ReadMore..]

### Linear Secret Sharing Schemes From Error Correcting Codes And ...

Choosing the error correcting codes and universal hash functions involved carefully, we obtain solutions to the following open problems: – A linear near- ... [ReadMore..]

### Error–correcting Codes With Linear Algebra

Error–correcting codes with linear algebra. Jeff Jauregui. August 24, 2012. 1 The problem. Consider a situation in which you must transmit a binary data ... [ReadMore..]

### Efficient Linear And Affine Codes For Correcting Insertions/Deletions

This paper studies \emph{linear} and \emph{affine} error-correcting codes for correcting synchronization errors such as insertions and deletions. We call such codes linear/affine insdel codes. Linear codes that can correct even a single deletion are limited to have information rate at most $1/2$ (achieved by the trivial 2-fold repetition code). Previously, it was (erroneously) reported that more generally no non-trivial linear codes correcting $k$ deletions exist, i.e., that the $(k+1)$-fold repetition codes and its rate of $1/(k+1)$ are basically optimal for any $k$. We disprove this and show the existence of binary linear codes of length $n$ and rate just below $1/2$ capable of correcting $Ω(n)$ insertions and deletions. This identifies rate $1/2$ as a sharp threshold for recovery from deletions for linear codes, and reopens the quest for a better understanding of the capabilities of linear codes for correcting insertions/deletions. We prove novel outer bounds and existential inner bounds for the rate Jul 17, 2020 ... This paper studies \emph{linear} and \emph{affine} error-correcting codes for correcting synchronization errors such as insertions and deletions ... [ReadMore..]

### Notes 1: Introduction, Linear Codes

Correcting single errors with the Hamming code: Suppose that y is a corrupted version of some (unknown) codeword c ∈ CHam, with a single bit flipped. We know ... [ReadMore..]

### Error-Correcting Linear Codes | SpringerLink

About this book. This text offers a thorough introduction to the mathematical concepts behind the theory of error-correcting linear codes. Care is taken to ... [ReadMore..]

The pages related to linear error correcting codes are also listed below:

### Coding Theory: Linear-Error Correcting Codes 1 Basic Definitions

Coding Theory: Linear-Error Correcting Codes. Anna Dovzhik. Math 420: Advanced Linear Algebra. Spring 2014. Sharing data across channels, such as satellite, ... [ReadMore..]

### Linear Error Correcting Codes With Anytime Reliability

We consider rate R = k/n causal linear codes that map a sequence of k-dimensional binary vectors {b_t} to a sequence of n-dimensional binary vectors {c_t}, such that each c_t is a function of {b_1,b_2,...,b_t}. Such a code is called anytime reliable, for a particular binary-input memoryless channel, if at each time, probability of making an error about a source bit that was sent d time instants ago decays exponentially in d. Anytime reliable codes are useful in interactive communication problems and, in particular, can be used to stabilize unstable plants across noisy channels. Schulman proved the existence of such codes which, due to their structure, he called tree codes; however, to date, no explicit constructions and tractable decoding algorithms have been devised. In this paper, we show the existence of anytime reliable "linear" codes with "high probability", i.e., suitably chosen random linear causal codes are anytime reliable with high probability. The key is to consider time-invariant codes (i.e., ones Feb 17, 2011 ... Such a code is called anytime reliable, for a particular binary-input memoryless channel, if at each time, probability of making an error ... [ReadMore..]