MinT - Information on Result #1837919

Information on Result #1837919

OOA(128⁷⁰, 2621440, S₁₂₈, 4, 15), using OOA 2-folding based on OOA(128⁷⁰, 5242880, S₁₂₈, 2, 15), using

discarding factors based on OOA(128⁷⁰, 5242881, S₁₂₈, 2, 15), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(128²⁰, 1048580, F₁₂₈, 2, 7) (dual of [(1048580, 2), 2097140, 8]-NRT-code), using
    - OOA 2-folding [i] based on linear OA(128²⁰, 2097160, F₁₂₈, 7) (dual of [2097160, 2097140, 8]-code), using
      - constructionÂ X applied to C([0,3]) âŠ‚ C([0,2]) [i] based on
        linear OA(128¹⁹, 2097153, F₁₂₈, 7) (dual of [2097153, 2097134, 8]-code), using the expurgated narrow-sense BCH-code C(I) with length 2097153Â | 128⁶âˆ’1, defining interval IÂ =Â [0,3], and minimum distance dÂ â‰¥ |{−3,−2,…,3}|+1Â =Â 8 (BCH-bound) [i]
        linear OA(128¹³, 2097153, F₁₂₈, 5) (dual of [2097153, 2097140, 6]-code), using the expurgated narrow-sense BCH-code C(I) with length 2097153Â | 128⁶âˆ’1, defining interval IÂ =Â [0,2], and minimum distance dÂ â‰¥ |{−2,−1,0,1,2}|+1Â =Â 6 (BCH-bound) [i]
        linear OA(128¹, 7, F₁₂₈, 1) (dual of [7, 6, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(128¹, s, F₁₂₈, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [i]
  2. OOA(128⁵⁰, 4194301, S₁₂₈, 2, 15), using
    - OOA 2-folding [i] based on OA(128⁵⁰, 8388602, S₁₂₈, 15), using
      - discarding factors based on OA(128⁵⁰, large, S₁₂₈, 15), using
        discarding parts of the base [i] based on linear OA(256⁴³, large, F₂₅₆, 15) (dual of [large, large−43, 16]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 256³âˆ’1, defining interval IÂ =Â [0,14], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [i]

Mode: Constructive.

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.