Geodesic
Comparison of the binary Golay code with the algebro-geometric code
Prikladnaâ diskretnaâ matematika, no. 4 (2015), pp. 77-82

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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.
Mots-clés : $AG$-code, $L$-construction
Keywords: Golay code, elliptic curve. 
@article{PDM_2015_4_a6,
     author = {P. M. Shiriaev},
     title = {Comparison of the binary {Golay} code with the algebro-geometric code},
     journal = {Prikladna\^a diskretna\^a matematika},
     pages = {77--82},
     publisher = {mathdoc},
     number = {4},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDM_2015_4_a6/}
}
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P. M. Shiriaev. Comparison of the binary Golay code with the algebro-geometric code. Prikladnaâ diskretnaâ matematika, no. 4 (2015), pp. 77-82. http://geodesic.mathdoc.fr/item/PDM_2015_4_a6/