This article is cited in 1 paper

Applied Coding Theory

Comparison of the binary Golay code with the algebro-geometric code

P. M. Shiriaev

Lomonosov Moscow State University, Moscow, Russia

Abstract: The binary Golay code $\mathcal G=[23,12,7]_2$ and a binary algebro-geometric code $C$, proposed by the author, are considered for coding information in a binary symmetric channel with bandwidth $W=50$ KB/s, coder/decoder clock rate $1$ GHz, bit error ratio $p=0.005$, and required decoding probability $0.9999$. It is shown that both codes fit this channel and the code $C$ rate is 12 % greater than the code $\mathcal G$ rate. It is also shown how you can increase the decoding speed of the standard decoding algorithm by a proper choice of a divisor $D$ and the basis of $L(D)$ for constructing $C$. The decoding complexity of $C$ is estimated and the message transmission durations for $C$ and $\mathcal G$ are compared.

Keywords: $AG$-code, Golay code, $L$-construction, elliptic curve.

UDC: 519.72

DOI: 10.17223/20710410/30/7

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