MinT - Information on Result #671914

Information on Result #671914

Linear OA(3²⁰², 209, F₃, 128) (dual of [209, 7, 129]-code), using juxtaposition based on

linear OA(3²⁰, 27, F₃, 14) (dual of [27, 7, 15]-code), using
- an extension C_e(13) of the primitive narrow-sense BCH-code C(I) with length 26Â = 3³âˆ’1, defining interval IÂ =Â [1,13], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 14 [i]
linear OA(3¹⁷⁵, 182, F₃, 113) (dual of [182, 7, 114]-code), using
- juxtaposition [i] based on
  1. linear OA(3⁷, 14, F₃, 5) (dual of [14, 7, 6]-code), using
    - extended quadratic residue code Q_e(14,3) [i]
  2. linear OA(3¹⁶¹, 168, F₃, 107) (dual of [168, 7, 108]-code), using
    - (u,Â uâˆ’v,Â u+v+w)-construction [i] based on
      1. linear OA(3⁵⁰, 56, F₃, 35) (dual of [56, 6, 36]-code), using
        dual code (with bound on d by constructionÂ Y1) [i] based on
        linear OA(3⁶, 56, F₃, 3) (dual of [56, 50, 4]-code or 56-cap in PG(5,3)), using
        the Hill cap [i]
        nonexistence of linear OA(3⁵, 21, F₃, 3) (dual of [21, 16, 4]-code or 21-cap in PG(4,3)), because
        20 is the largest size of a cap in PG(4,Â 3) [i]
      2. linear OA(3⁵⁵, 56, F₃, 53) (dual of [56, 1, 54]-code), using
        strength reduction [i] based on linear OA(3⁵⁵, 56, F₃, 55) (dual of [56, 1, 56]-code or 56-arc in PG(54,3)), using
        dual of repetition code with length 56 [i]
      3. linear OA(3⁵⁶, 56, F₃, 56) (dual of [56, 0, 57]-code or 56-arc in PG(55,3)), using
        complete OA / dual of code with only one code word [i]

Mode: Constructive and linear.

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