MinT - Information on Result #1019131

Information on Result #1019131

Linear OOA(128⁵², 5608658, F₁₂₈, 3, 9) (dual of [(5608658, 3), 16825922, 10]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(128¹³, 4194301, F₁₂₈, 3, 4) (dual of [(4194301, 3), 12582890, 5]-NRT-code), using
- OA 2-folding and stacking [i] based on linear OA(128¹³, 8388602, F₁₂₈, 4) (dual of [8388602, 8388589, 5]-code), using
  - discarding factors / shortening the dual code based on linear OA(128¹³, large, F₁₂₈, 4) (dual of [large, large−13, 5]-code), using
    - the expurgated narrow-sense BCH-code C(I) with length 17895697Â | 128⁴âˆ’1, defining interval IÂ =Â [0,3], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 5 [i]
linear OOA(128³⁹, 2804329, F₁₂₈, 3, 9) (dual of [(2804329, 3), 8412948, 10]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(128⁶, 8128, F₁₂₈, 3, 4) (dual of [(8128, 3), 24378, 5]-NRT-code), using
    - OA 2-folding and stacking [i] based on linear OA(128⁶, 16256, F₁₂₈, 4) (dual of [16256, 16250, 5]-code), using
      - 1 times truncation [i] based on linear OA(128⁷, 16257, F₁₂₈, 5) (dual of [16257, 16250, 6]-code), using
        a code by Danev and Olsson [i]
  2. linear OOA(128³³, 2796201, F₁₂₈, 3, 9) (dual of [(2796201, 3), 8388570, 10]-NRT-code), using
    - OOA 3-folding [i] based on linear OA(128³³, large, F₁₂₈, 9) (dual of [large, large−33, 10]-code), using
      - the expurgated narrow-sense BCH-code C(I) with length 15790321Â | 128⁸âˆ’1, defining interval IÂ =Â [0,4], and minimum distance dÂ â‰¥ |{−4,−3,…,4}|+1Â =Â 10 (BCH-bound) [i]

Mode: Constructive and linear.

Optimality

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

Other Results with Identical Parameters

None.

Depending Results

None.