MinT - Information on Result #640983

Information on Result #640983

Linear OA(3¹³⁷, 144, F₃, 86) (dual of [144, 7, 87]-code), using juxtaposition based on

linear OA(3⁵⁶, 63, F₃, 35) (dual of [63, 7, 36]-code), using
- discarding factors / shortening the dual code based on linear OA(3⁵⁶, 64, F₃, 35) (dual of [64, 8, 36]-code), using
  - concatenation of two codes [i] based on
    1. linear OA(9¹², 16, F₉, 11) (dual of [16, 4, 12]-code), using
      - extended algebraic-geometric code AG_e(F,4P) [i] based on function field F/F₉ with g(F) = 1 and N(F) ≥ 16, using
        a function field by GarcÃa and Quoos [i]
    2. linear OA(3², 4, F₃, 2) (dual of [4, 2, 3]-code or 4-arc in PG(1,3)), using
      - extended Reedâ€“Solomon code RS_e(2,3) [i]
      - Hamming code H(2,3) [i]
      - Simplex code S(2,3) [i]
      - the Tetracode [i]
linear OA(3⁷⁴, 81, F₃, 50) (dual of [81, 7, 51]-code), using
- an extension C_e(49) of the primitive narrow-sense BCH-code C(I) with length 80Â = 3⁴âˆ’1, defining interval IÂ =Â [1,49], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 50 [i]

Mode: Constructive and linear.

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