MinT - Information on Result #1297237

Information on Result #1297237

Linear OA(2¹¹⁸, 205, F₂, 32) (dual of [205, 87, 33]-code), using constructionÂ X with VarÅ¡amov bound based on

linear OA(2¹¹², 197, F₂, 32) (dual of [197, 85, 33]-code), using
- 1 times truncation [i] based on linear OA(2¹¹³, 198, F₂, 33) (dual of [198, 85, 34]-code), using
  - concatenation of two codes [i] based on
    1. linear OA(32¹⁶, 33, F₃₂, 16) (dual of [33, 17, 17]-code or 33-arc in PG(15,32)), using
      - extended Reedâ€“Solomon code RS_e(17,32) [i]
    2. linear OA(2¹, 6, F₂, 1) (dual of [6, 5, 2]-code), using
      - discarding factors / shortening the dual code based on linear OA(2¹, s, F₂, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [i]
linear OA(2¹¹², 199, F₂, 28) (dual of [199, 87, 29]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 2¹¹²Â > V_b^sâˆ’1(kâˆ’1)Â = 1736 908582 643113 687840 364235 166512 [i]
linear OA(2⁴, 6, F₂, 3) (dual of [6, 2, 4]-code or 6-cap in PG(3,2)), using
- discarding factors / shortening the dual code based on linear OA(2⁴, 7, F₂, 3) (dual of [7, 3, 4]-code or 7-cap in PG(3,2)), using
  - Simplex code S(3,2) [i]

Mode: Linear.

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