MinT - Information on Result #908571

Information on Result #908571

Linear OOA(2¹⁸⁸, 98, F₂, 2, 97) (dual of [(98, 2), 8, 98]-NRT-code), using juxtaposition based on

linear OOA(2⁶⁴, 36, F₂, 2, 35) (dual of [(36, 2), 8, 36]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(2²⁹, 18, F₂, 2, 17) (dual of [(18, 2), 7, 18]-NRT-code), using
    - (u,Â u+v)-construction [i] based on
      1. linear OOA(2¹², 10, F₂, 2, 8) (dual of [(10, 2), 8, 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]
  2. linear OOA(2³⁵, 18, F₂, 2, 35) (dual of [(18, 2), 1, 36]-NRT-code), using
    - dual of repetition NRT-code with length 18 [i]
linear OOA(2¹¹⁶, 62, F₂, 2, 61) (dual of [(62, 2), 8, 62]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(2⁵⁵, 31, F₂, 2, 30) (dual of [(31, 2), 7, 31]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(2⁵⁵, 32, F₂, 2, 30) (dual of [(32, 2), 9, 31]-NRT-code), using
      - 2 times NRT-code embedding in larger space [i] based on linear OOA(2⁵¹, 30, F₂, 2, 30) (dual of [(30, 2), 9, 31]-NRT-code), using
        strength reduction [i] based on linear OOA(2⁵¹, 30, F₂, 2, 31) (dual of [(30, 2), 9, 32]-NRT-code), using
        concatenation of two NRT-codes [i] based on
        linear OA(8⁷, 10, F₈, 7) (dual of [10, 3, 8]-code or 10-arc in PG(6,8)), using
        Denniston code D(1,8) [i]
        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]
  2. linear OOA(2⁶¹, 31, F₂, 2, 61) (dual of [(31, 2), 1, 62]-NRT-code), using
    - dual of repetition NRT-code with length 31 [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.