MinT - Information on Result #1298823

Information on Result #1298823

Linear OA(3¹⁶⁵, 190, F₃, 81) (dual of [190, 25, 82]-code), using constructionÂ X with VarÅ¡amov bound based on

linear OA(3¹⁶³, 187, F₃, 81) (dual of [187, 24, 82]-code), using
- 2 times truncation [i] based on linear OA(3¹⁶⁵, 189, F₃, 83) (dual of [189, 24, 84]-code), using
  - concatenation of two codes [i] based on
    1. linear OA(27¹³, 21, F₂₇, 13) (dual of [21, 8, 14]-code or 21-arc in PG(12,27)), using
      - discarding factors / shortening the dual code based on linear OA(27¹³, 27, F₂₇, 13) (dual of [27, 14, 14]-code or 27-arc in PG(12,27)), using
        Reedâ€“Solomon code RS(14,27) [i]
    2. linear OA(3⁶, 9, F₃, 5) (dual of [9, 3, 6]-code), using
      - discarding factors / shortening the dual code based on linear OA(3⁶, 10, F₃, 5) (dual of [10, 4, 6]-code), using
        projective code from ovoid in PG(3,Â 3) [i]
linear OA(3¹⁶³, 188, F₃, 79) (dual of [188, 25, 80]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 3¹⁶³Â > V_b^sâˆ’1(kâˆ’1)Â = 408075 009880 220948 948276 048884 014770 570235 826145 816465 649953 332174 716465 890619 [i]
linear OA(3¹, 2, F₃, 1) (dual of [2, 1, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(3¹, s, F₃, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
  - parity-check code [i]

Mode: Linear.

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