MinT - Information on Result #1298088

Information on Result #1298088

Linear OA(3⁷², 116, F₃, 28) (dual of [116, 44, 29]-code), using constructionÂ X with VarÅ¡amov bound based on

linear OA(3⁶⁹, 111, F₃, 28) (dual of [111, 42, 29]-code), using
- 1 times truncation [i] based on linear OA(3⁷⁰, 112, F₃, 29) (dual of [112, 42, 30]-code), using
  - concatenation of two codes [i] based on
    1. linear OA(27¹⁴, 28, F₂₇, 14) (dual of [28, 14, 15]-code or 28-arc in PG(13,27)), using
      - extended Reedâ€“Solomon code RS_e(14,27) [i]
    2. linear OA(3¹, 4, F₃, 1) (dual of [4, 3, 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]
linear OA(3⁶⁹, 113, F₃, 26) (dual of [113, 44, 27]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 3⁶⁹Â > V_b^sâˆ’1(kâˆ’1)Â = 235 877878 232297 879046 434717 283009 [i]
linear OA(3¹, 3, F₃, 1) (dual of [3, 2, 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 (see above)

Mode: Linear.

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