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Constructing rate 1/p systematic binary quasi-cyclic codes based on the matroid theory

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Abstract

In this paper, rate 1/p binary systematic quasi-cyclic (QC) codes are constructed based on Matroid Theory (MT). The relationship between the generator matrix and minimum distance d is derived through MT, which is benefit to find numbers of QC codes with large minimum distance by our Matroid search algorithm. More than seventy of QC codes that extend previously published results are presented. Among these codes, there are nine codes whose minimum distance is larger than those of the known codes found by Gulliver et al.

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Authors and Affiliations

  1. Department of Communication Engineering, College of Information Science and Technology, Xiamen University, Xiamen, 361005, Fujian Province, China

    Guangfu Wu & Lin Wang

  2. Department of Information Engineering, I-Shou University, Kaohsiung, Taiwan

    Hsin-Chiu Chang & T. K. Truong

  3. Department of Computer Science and Engineering, National Sun Yat-Sen University, Kaohsiung, Taiwan

    T. K. Truong

Authors
  1. Guangfu Wu
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  2. Hsin-Chiu Chang
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  3. Lin Wang
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  4. T. K. Truong
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Corresponding author

Correspondence to Lin Wang.

Additional information

Communicated by J.-L. Kim.

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Wu, G., Chang, HC., Wang, L. et al. Constructing rate 1/p systematic binary quasi-cyclic codes based on the matroid theory. Des. Codes Cryptogr. 71, 47–56 (2014). https://doi.org/10.1007/s10623-012-9715-1

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  • DOI: https://doi.org/10.1007/s10623-012-9715-1

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