MinT - Information on Result #641471

Information on Result #641471

Linear OA(8⁸⁴, 88, F₈, 70) (dual of [88, 4, 71]-code), using juxtaposition based on

linear OA(8⁸, 12, F₈, 7) (dual of [12, 4, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(8⁸, 14, F₈, 7) (dual of [14, 6, 8]-code), using
  - extended algebraic-geometric code AG_e(F,6P) [i] based on function field F/F₈ with g(F) = 1 and N(F) ≥ 14, using
    - F₂ from the tower of function fields over F₈ by van der Geer and van der Vlugt [i]
linear OA(8⁷², 76, F₈, 62) (dual of [76, 4, 63]-code), using
- juxtaposition [i] based on
  1. linear OA(8⁷, 11, F₈, 6) (dual of [11, 4, 7]-code), using
    - discarding factors / shortening the dual code based on linear OA(8⁷, 14, F₈, 6) (dual of [14, 7, 7]-code), using
      - extended algebraic-geometric code AG_e(F,7P) [i] based on function field F/F₈ with g(F) = 1 and N(F) ≥ 14 (see above)
  2. linear OA(8⁶¹, 65, F₈, 55) (dual of [65, 4, 56]-code), using
    - projective code from ovoid in PG(3,Â 8) [i]
    - the expurgated narrow-sense BCH-code C(I) with length 65Â | 8⁴âˆ’1, defining interval IÂ =Â [0,27], and minimum distance dÂ â‰¥ |{−27,−26,…,27}|+1Â =Â 56 (BCH-bound) [i]

Mode: Constructive and linear.

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