Geodesic
Comparison of the binary Golay code with the algebro-geometric code
Prikladnaâ diskretnaâ matematika, no. 4 (2015), pp. 77-82 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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     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},
     year = {2015},
     number = {4},
     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/

[1] Vleduts S. G., Nogin D. Yu., Tsfasman M. A., Algebro-Geometric Codes. Basic Concepts, MCCME Publ., Moscow, 2002, 504 pp. (in Russian)

[2] Semenovykh D. N., On Number-Theoretic Problems in Coding Theory, PhD Thesis, MSU Publ., Moscow, 2005, 60 pp. (in Russian)

[3] Menezes A., Wu Y.-H., Zuccherato R., An Elementary Introduction to Hyperelliptic Curves, Research report No. 19, Faculty of Mathematics, University of Waterloo, Waterloo, 1996, 35 pp.

[4] Bogachev K. Yu., Workshop on the Computer. Methods for Linear Systems Solving and Eigenvalues Finding, MSU Publ., Moscow, 1998, 79 pp. (in Russian)

[5] Mak-Vil'yams F. Dzh., Sloen N. Dzh. A., The Theory of Error-Correcting Codes, Svyaz' Publ., Moscow, 1979, 774 pp. (in Russian)