MinT - Information on Result #2212852

Information on Result #2212852

Linear OA(8⁸⁵, 89, F₈, 70) (dual of [89, 4, 71]-code), using strength reduction based on linear OA(8⁸⁵, 89, F₈, 71) (dual of [89, 4, 72]-code), using

juxtaposition [i] based on
1. 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]
2. linear OA(8⁷³, 77, F₈, 63) (dual of [77, 4, 64]-code), using
  - juxtaposition [i] based on
    1. linear OA(8⁸, 12, F₈, 7) (dual of [12, 4, 8]-code) (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.

Optimality

Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.

Compare with Markus Grassl’s online database of code parameters.

Other Results with Identical Parameters

None.

Depending Results

None.