MinT - Information on Result #1298142

Information on Result #1298142

Linear OA(3⁸¹, 116, F₃, 34) (dual of [116, 35, 35]-code), using constructionÂ X with VarÅ¡amov bound based on

linear OA(3⁷⁸, 111, F₃, 34) (dual of [111, 33, 35]-code), using
- 1 times truncation [i] based on linear OA(3⁷⁹, 112, F₃, 35) (dual of [112, 33, 36]-code), using
  - concatenation of two codes [i] based on
    1. linear OA(27¹⁷, 28, F₂₇, 17) (dual of [28, 11, 18]-code or 28-arc in PG(16,27)), using
      - extended Reedâ€“Solomon code RS_e(11,27) [i]
      - the expurgated narrow-sense BCH-code C(I) with length 28Â | 27²âˆ’1, defining interval IÂ =Â [0,8], and minimum distance dÂ â‰¥ |{−8,−7,…,8}|+1Â =Â 18 (BCH-bound) [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(3⁷⁸, 113, F₃, 32) (dual of [113, 35, 33]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 3⁷⁸Â > V_b^sâˆ’1(kâˆ’1)Â = 10 943120 867743 353547 691133 406856 983233 [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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