Asymmetric Single Magnitude Four Error Correcting Codes

New single asymmetric error-correcting codes

New single asymmetric error-correcting codes are proposed. These codes are better than existing codes when the code length n is greater than 10, except for n = 12 and n = 15. In many cases one can construct a code C containing at least d2=ne codewords. It is known that a code with jCj d2=(n + 1)e can be easily obtained. It should be noted that the proposed codes for n = 12 and n = 15 are also t...

Asymmetric quantum error correcting codes

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Two New Four-Error-Correcting Binary Codes

Gallager error-correcting codes for binary asymmetric channels

Abstract. We derive critical noise levels for Gallager codes on asymmetric channels as a function of the input bias and the temperature. Using a statistical mechanics approach we study the space of codewords and the entropy in the various decoding regimes. We further discuss the relation of the convergence of the message passing algorithm with the endogenous property and complexity, characteriz...

Some codes correcting single symmetric errors of limited magnitude

An error model with symmetric errors of limited magnitude is considered. Limited magnitude means that the size of any error is limited by a number smaller (usually much smaller) than the alphabet size. Several constructions of codes correcting single error are given. In some cases, the codes are perfect or quasi-perfect.