MinT - Information on Result #1298128

Information on Result #1298128

Linear OA(3⁷⁸, 116, F₃, 32) (dual of [116, 38, 33]-code), using constructionÂ X with VarÅ¡amov bound based on

linear OA(3⁷⁵, 111, F₃, 32) (dual of [111, 36, 33]-code), using
- 1 times truncation [i] based on linear OA(3⁷⁶, 112, F₃, 33) (dual of [112, 36, 34]-code), using
  - concatenation of two codes [i] based on
    1. linear OA(27¹⁶, 28, F₂₇, 16) (dual of [28, 12, 17]-code or 28-arc in PG(15,27)), using
      - extended Reedâ€“Solomon code RS_e(12,27) [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(3⁷⁵, 113, F₃, 30) (dual of [113, 38, 31]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 3⁷⁵Â > V_b^sâˆ’1(kâˆ’1)Â = 366552 888864 694862 278436 258692 313793 [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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