In this paper, we present a novel class of forward error correcting codes constructed using the discrete Walsh transform. They are a class of double-error correcting codes defined on the field of real numbers. An iterative decoding algorithm for Walsh transform codes is developed and implemented. The error correcting performance of Walsh transform codes over an AWGN channel is evaluated. Select...

It is clarified whether or not “full rank perfect 1-error correcting binary codes act like primes in the family of all perfect 1-error correcting binary codes”. Thereby the well known connection between perfect 1-error correcting binary codes and tilings will be discussed and used.

We give an algorithm for constructing linear network error-correcting codes that achieve the Singleton bound for network error-correcting codes. The proposed algorithm is based on the algorithm by Jaggi et al. We also clarify the relationship between the robust network coding and the network error-correcting codes with known locations of errors.

In this survey we describe relations between classical and quantum error{correcting codes. After a brief introduction to both quantum computation and classical linear error{correcting codes, we show how to construct quantum error{correcting codes based on classical ones. Furthermore, quantum circuits for encoding and syndrome computation are presented.

computational errors in numerical data processing may be detected efficiently by using parity values associated with real number codes, even when inherent round off errors are allowed in addition to failure disruptions. this paper examines correcting turbo codes by straightforward application of an algorithm derived for finite-field codes, modified to operate over any field. there are syndromes...

In this correspondence, we study binary asymmetric errorcorrecting codes. A general construction for binary asymmetric error-correcting codes is presented. We show that some previously known lower bounds for binary asymmetric error-correcting codes can be obtained from this general construction. Furthermore, some new lower bounds for binary asymmetric error-correcting codes are obtained from th...

In this correspondence, we study binary asymmetric errorcorrecting codes. A general construction for binary asymmetric error-correcting codes is presented. We show that some previously known lower bounds for binary asymmetric error-correcting codes can be obtained from this general construction. Furthermore, some new lower bounds for binary asymmetric error-correcting codes are obtained from th...

The possibility of using the twofold topological degeneracy of spin-1/2 chiral spin liquid states on the torus to construct quantum error-correcting codes is investigated. It is shown that codes constructed using these states on finite periodic lattices do not meet the necessary and sufficient conditions for correcting even a single qubit error with perfect fidelity. However, for large enough l...