MinT - Information on Result #2808595

Information on Result #2808595

OOA(128⁶⁹, 2101247, S₁₂₈, 4, 16), using 128¹ times duplication based on OOA(128⁶⁸, 2101247, S₁₂₈, 4, 16), using

OOA 2-folding [i] based on OOA(128⁶⁸, 4202494, S₁₂₈, 2, 16), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(128¹⁵, 8193, F₁₂₈, 2, 8) (dual of [(8193, 2), 16371, 9]-NRT-code), using
    - OOA 2-folding [i] based on linear OA(128¹⁵, 16386, F₁₂₈, 8) (dual of [16386, 16371, 9]-code), using
      - constructionÂ X applied to C_e(7) âŠ‚ C_e(6) [i] based on
        linear OA(128¹⁵, 16384, F₁₂₈, 8) (dual of [16384, 16369, 9]-code), using an extension C_e(7) of the primitive narrow-sense BCH-code C(I) with length 16383Â = 128²âˆ’1, defining interval IÂ =Â [1,7], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 8 [i]
        linear OA(128¹³, 16384, F₁₂₈, 7) (dual of [16384, 16371, 8]-code), using an extension C_e(6) of the primitive narrow-sense BCH-code C(I) with length 16383Â = 128²âˆ’1, defining interval IÂ =Â [1,6], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]
        linear OA(128⁰, 2, F₁₂₈, 0) (dual of [2, 2, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(128⁰, s, F₁₂₈, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
        OA with only one run / dual of code without redundancy [i]
  2. OOA(128⁵³, 4194301, S₁₂₈, 2, 16), using
    - OOA 2-folding [i] based on OA(128⁵³, 8388602, S₁₂₈, 16), using
      - discarding factors based on OA(128⁵³, large, S₁₂₈, 16), using
        discarding parts of the base [i] based on linear OA(256⁴⁶, large, F₂₅₆, 16) (dual of [large, large−46, 17]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 256³âˆ’1, defining interval IÂ =Â [0,15], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [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.