MinT - Information on Result #662281

Information on Result #662281

Linear OA(4²³⁴, 65567, F₄, 35) (dual of [65567, 65333, 36]-code), using (u,Â u+v)-construction based on

linear OA(4²⁵, 30, F₄, 17) (dual of [30, 5, 18]-code), using
- (u,Â uâˆ’v,Â u+v+w)-construction [i] based on
  1. linear OA(4⁶, 10, F₄, 5) (dual of [10, 4, 6]-code), using
    - discarding factors / shortening the dual code based on linear OA(4⁶, 12, F₄, 5) (dual of [12, 6, 6]-code), using
      - extended quadratic residue code Q_e(12,4) [i]
  2. linear OA(4⁹, 10, F₄, 8) (dual of [10, 1, 9]-code), using
    - strength reduction [i] based on linear OA(4⁹, 10, F₄, 9) (dual of [10, 1, 10]-code or 10-arc in PG(8,4)), using
      - dual of repetition code with length 10 [i]
  3. linear OA(4¹⁰, 10, F₄, 10) (dual of [10, 0, 11]-code or 10-arc in PG(9,4)), using
    - complete OA / dual of code with only one code word [i]
linear OA(4²⁰⁹, 65537, F₄, 35) (dual of [65537, 65328, 36]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 65537Â | 4¹⁶âˆ’1, defining interval IÂ =Â [0,17], and minimum distance dÂ â‰¥ |{−17,−16,…,17}|+1Â =Â 36 (BCH-bound) [i]

Mode: Constructive and linear.

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