MinT - Information on Result #908765

Information on Result #908765

Linear OOA(2¹²⁶, 66, F₂, 2, 68) (dual of [(66, 2), 6, 69]-NRT-code), using juxtaposition based on

linear OOA(2²⁴, 15, F₂, 2, 14) (dual of [(15, 2), 6, 15]-NRT-code), using
- strength reduction [i] based on linear OOA(2²⁴, 15, F₂, 2, 15) (dual of [(15, 2), 6, 16]-NRT-code), using
  - concatenation of two NRT-codes [i] based on
    1. linear OA(8³, 5, F₈, 3) (dual of [5, 2, 4]-code or 5-arc in PG(2,8) or 5-cap in PG(2,8)), using
      - discarding factors / shortening the dual code based on linear OA(8³, 8, F₈, 3) (dual of [8, 5, 4]-code or 8-arc in PG(2,8) or 8-cap in PG(2,8)), using
        Reedâ€“Solomon code RS(5,8) [i]
    2. linear OOA(2³, 3, F₂, 2, 3) (dual of [(3, 2), 3, 4]-NRT-code), using
      - extended Reedâ€“Solomon NRT-code RS_e(2;3,2) [i]
linear OOA(2⁹⁶, 51, F₂, 2, 53) (dual of [(51, 2), 6, 54]-NRT-code), using
- repeating each code word 3 times [i] based on linear OOA(2²⁸, 17, F₂, 2, 17) (dual of [(17, 2), 6, 18]-NRT-code), using
  - (u,Â u+v)-construction [i] based on
    1. linear OOA(2¹¹, 8, F₂, 2, 8) (dual of [(8, 2), 5, 9]-NRT-code), using
      - an explicit generator matrix by Edel [i]
    2. linear OOA(2¹⁷, 9, F₂, 2, 17) (dual of [(9, 2), 1, 18]-NRT-code), using
      - dual of repetition NRT-code with length 9 [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.

Other Results with Identical Parameters

None.

Depending Results

None.