MinT - Information on Result #1019207

Information on Result #1019207

Linear OOA(128⁶⁷, 5608916, F₁₂₈, 3, 11) (dual of [(5608916, 3), 16826681, 12]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(128¹⁷, 4194301, F₁₂₈, 3, 5) (dual of [(4194301, 3), 12582886, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(128¹⁷, large, F₁₂₈, 5) (dual of [large, large−17, 6]-code), using
  - the expurgated narrow-sense BCH-code C(I) with length 17895697Â | 128⁴âˆ’1, defining interval IÂ =Â [0,4], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 6 [i]
linear OOA(128⁵⁰, 2804458, F₁₂₈, 3, 11) (dual of [(2804458, 3), 8413324, 12]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(128⁹, 8257, F₁₂₈, 3, 5) (dual of [(8257, 3), 24762, 6]-NRT-code), using
    - (u,Â u+v)-construction [i] based on
      1. linear OOA(128², 129, F₁₂₈, 3, 2) (dual of [(129, 3), 385, 3]-NRT-code), using
        extended Reedâ€“Solomon NRT-code RS_e(3;385,128) [i]
      2. linear OOA(128⁷, 8128, F₁₂₈, 3, 5) (dual of [(8128, 3), 24377, 6]-NRT-code), using
        OOA 2-folding and stacking with additional row [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(128⁴¹, 2796201, F₁₂₈, 3, 11) (dual of [(2796201, 3), 8388562, 12]-NRT-code), using
    - OOA 3-folding [i] based on linear OA(128⁴¹, large, F₁₂₈, 11) (dual of [large, large−41, 12]-code), using
      - the expurgated narrow-sense BCH-code C(I) with length 15790321Â | 128⁸âˆ’1, defining interval IÂ =Â [0,5], and minimum distance dÂ â‰¥ |{−5,−4,…,5}|+1Â =Â 12 (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.