linear error-correcting codes used in communications. (14) I. S. Reed, “A class of multiple-errorcorrecting codes and the decoding scheme,” IRE. Trans. A class of multiple-error-correcting codes and the decoding scheme. more. less. I. Reed · Details · Authors · Fields of science · Bibliography · Quotations · Similar. linear error correcting codes used in communications (2).For bit study is to d...

In this document we analyze efficiency of a communication system that applies the error correction mechanism using retransmissions. Namely, the transmitter sends a block consisting of Nin information and Noh overhead bits, such that Nb = Nin + Noh. No forward error correction coding is applied. The transmission is performed using digital modulation, where R bits are transmitted per each modulat...

In this note we report two versions of Gilbert-Varshamov type existential bounds for asymmetric quantum error-correcting codes.

We consider structural vector error correction models (VECMs) in which permanent shocks are partially identified with a set of long-run restrictions, and fully identified with an additional set of short-run restrictions. An identification method with a combination of short-run and long-run restrictions has been studied in the vector autoregressive models literature, but not thoroughly applied t...

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We present a construction scheme for quantum error correcting codes. The basic ingredients are a graph and a finite abelian group, from which the code can explicitly be obtained. We prove necessary and sufficient conditions for the graph such that the resulting code corrects a certain number of errors. This allows a simple verification of the 1-error correcting property of fivefold codes in any...

Reed-Solomon codes are examples of error correcting codes, in which redundant information is added to data so that it can be recovered reliably despite errors in transmission or storage and retrieval. The error correction system used on CD’s and DVD’s is based on a Reed-Solomon code. These codes are also used on satellite links and other communications systems. We will first discuss the general...

We propose a linear optical scheme to transmit an unknown qubit robustly over bit-flip-error channel. To avoid the technical difficulty of the standard quantum error correction code, our scheme is based on the concept of errorrejection. The whole scheme is based on currently existing technology.

The problem of finding quantum-error-correcting codes is transformed into the problem of finding additive codes over the field GF (4) which are self-orthogonal with respect to a certain trace inner product. Many new codes and new bounds are presented, as well as a table of upper and lower bounds on such codes of length up to 30 qubits.