MinT - Information on Result #641083

Information on Result #641083

Linear OA(4¹⁶⁸, 175, F₄, 116) (dual of [175, 7, 117]-code), using juxtaposition based on

linear OA(4⁵⁴, 61, F₄, 40) (dual of [61, 7, 41]-code), using
- discarding factors / shortening the dual code based on linear OA(4⁵⁴, 62, F₄, 40) (dual of [62, 8, 41]-code), using
  - 3 times truncation [i] based on linear OA(4⁵⁷, 65, F₄, 43) (dual of [65, 8, 44]-code), using
    - the expurgated narrow-sense BCH-code C(I) with length 65Â | 4⁶âˆ’1, defining interval IÂ =Â [0,21], and minimum distance dÂ â‰¥ |{−21,−20,…,21}|+1Â =Â 44 (BCH-bound) [i]
linear OA(4¹⁰⁷, 114, F₄, 75) (dual of [114, 7, 76]-code), using
- discarding factors / shortening the dual code based on linear OA(4¹⁰⁷, 115, F₄, 75) (dual of [115, 8, 76]-code), using
  - concatenation of two codes [i] based on
    1. linear OA(16¹⁹, 23, F₁₆, 18) (dual of [23, 4, 19]-code), using
      - discarding factors / shortening the dual code based on linear OA(16¹⁹, 24, F₁₆, 18) (dual of [24, 5, 19]-code), using
        extended algebraic-geometric code AG_e(F,5P) [i] based on function field F/F₁₆ with g(F) = 1 and N(F) ≥ 24, using
        a function field by SÃ©mirat [i]
    2. linear OA(4³, 5, F₄, 3) (dual of [5, 2, 4]-code or 5-arc in PG(2,4) or 5-cap in PG(2,4)), using
      - extended Reedâ€“Solomon code RS_e(2,4) [i]
      - Simplex code S(2,4) [i]

Mode: Constructive and linear.

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None.