On a Greedy Algorithm for Generating Ordered Basis and Linear Codes Generated by the Algorithm

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Bibliographic Information

Other Title
  • 貪欲法に基づく順序付基底を構成するアルゴリズムと生成される線形符号について

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Description

The paper presents an algorithm for generating an ordered basis of F^n_q, where F_q is the finite field with q-elements. The purpose of the algorithm is to construct a linear code with a large Feng-Rao designed distance d_<FR>. In order to obtain a linear code with a large d_<FR>, we need to construct a good ordered basis. The ordered basis is an indexed basis of F^n_q. The proposed algorithm improves an initial basis for each step of the algorithm according to a heuristic rule. The time complexity of the algorithm is O(n^4). The algorithm can work for arbitrary finite field, length, dimension. The linear codes obtained from the algorithm can be decoded up to ⌊(d_<FR>-1)/2⌋ with time complexity O(n^3). Some high rate codes obtained by the algorithm are comparable to the improved Geometric Goppa codes.

Journal

  • Technical report of IEICE. ISEC

    Technical report of IEICE. ISEC 98 (656), 113-118, 1999-03-11

    The Institute of Electronics, Information and Communication Engineers

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Details 詳細情報について

  • CRID
    1573950402106366208
  • NII Article ID
    110003297452
  • NII Book ID
    AN10060811
  • Text Lang
    ja
  • Data Source
    • CiNii Articles

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