MinT - Information on Result #2808583

Information on Result #2808583

OOA(128⁶⁷, 2118997, S₁₂₈, 4, 15), using 128¹ times duplication based on OOA(128⁶⁶, 2118997, S₁₂₈, 4, 15), using

(u,Â u+v)-construction [i] based on
1. OOA(128¹⁶, 21847, S₁₂₈, 4, 7), using
  - OOA 3-folding and stacking with additional row [i] based on OA(128¹⁶, 65542, S₁₂₈, 7), using
    - discarding parts of the base [i] based on linear OA(256¹⁴, 65542, F₂₅₆, 7) (dual of [65542, 65528, 8]-code), using
      - constructionÂ X applied to C([0,3]) âŠ‚ C([0,2]) [i] based on
        linear OA(256¹³, 65537, F₂₅₆, 7) (dual of [65537, 65524, 8]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537Â | 256⁴âˆ’1, defining interval IÂ =Â [0,3], and minimum distance dÂ â‰¥ |{−3,−2,…,3}|+1Â =Â 8 (BCH-bound) [i]
        linear OA(256⁹, 65537, F₂₅₆, 5) (dual of [65537, 65528, 6]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537Â | 256⁴âˆ’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(256¹, 5, F₂₅₆, 1) (dual of [5, 4, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(256¹, s, F₂₅₆, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [i]
2. OOA(128⁵⁰, 2097150, S₁₂₈, 4, 15), using
  - OOA 4-folding [i] based on OA(128⁵⁰, 8388600, 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.