MinT - Information on Result #1837892

Information on Result #1837892

OOA(128⁶¹, 2113535, S₁₂₈, 4, 14), using OOA 2-folding based on OOA(128⁶¹, 4227070, S₁₂₈, 2, 14), using

(u,Â u+v)-construction [i] based on
1. OOA(128¹⁵, 32769, S₁₂₈, 2, 7), using
  - OOA 2-folding [i] based on OA(128¹⁵, 65538, S₁₂₈, 7), using
    - discarding parts of the base [i] based on linear OA(256¹³, 65538, F₂₅₆, 7) (dual of [65538, 65525, 8]-code), using
      - constructionÂ X applied to C_e(6) âŠ‚ C_e(5) [i] based on
        linear OA(256¹³, 65536, F₂₅₆, 7) (dual of [65536, 65523, 8]-code), using an extension C_e(6) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,6], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]
        linear OA(256¹¹, 65536, F₂₅₆, 6) (dual of [65536, 65525, 7]-code), using an extension C_e(5) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,5], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 6 [i]
        linear OA(256⁰, 2, F₂₅₆, 0) (dual of [2, 2, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(256⁰, s, F₂₅₆, 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(128⁴⁶, 4194301, S₁₂₈, 2, 14), using
  - OOA 2-folding [i] based on OA(128⁴⁶, 8388602, S₁₂₈, 14), using
    - discarding factors based on OA(128⁴⁶, large, S₁₂₈, 14), using
      - discarding parts of the base [i] based on linear OA(256⁴⁰, large, F₂₅₆, 14) (dual of [large, large−40, 15]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 256³âˆ’1, defining interval IÂ =Â [0,13], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 15 [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.