Abstract
By employing a certain multiplicative group in the rational function field and places of degree one and two, we present a construction of binary linear codes in this paper. One feature is that the minimum distance of the code is bounded via the Hurwitz genus formula of function fields. It turns out that many optimal and best-known binary linear codes are obtained through our construction.
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Acknowledgments
The authors would like to thank the referees for many helpful comments. The research work of the first author is supported in part by Shanghai Sailing Program under the Grant 15YF1401200 and by the National Natural Science Foundation of China under Grant 11501117. The research work of the second author is supported in part by the Shanghai Excellent Academic Leader Funds under Grant 16XD1400200 and the Basic Research of Shanghai Science and Technology Innovation Plan under Grant 16JC1402700.
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Communicated by C. Mitchell.
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Jin, L., Kan, H. Construction of binary linear codes via rational function fields. Des. Codes Cryptogr. 83, 633–638 (2017). https://doi.org/10.1007/s10623-016-0252-1
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DOI: https://doi.org/10.1007/s10623-016-0252-1