MinT - Information on Result #1837778

Information on Result #1837778

OOA(128²⁷, 2861737, S₁₂₈, 4, 7), using OOA stacking with additional row based on OOA(128²⁷, 2861738, S₁₂₈, 3, 7), using

(u,Â u+v)-construction [i] based on
1. OOA(128⁵, 65537, S₁₂₈, 3, 3), using
  - appending kth column [i] based on OOA(128⁵, 65537, S₁₂₈, 2, 3), using
    - discarding parts of the base [i] based on linear OOA(256⁴, 65537, F₂₅₆, 2, 3) (dual of [(65537, 2), 131070, 4]-NRT-code), using
      - OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(256⁴, 65537, F₂₅₆, 3) (dual of [65537, 65533, 4]-code or 65537-cap in PG(3,256)), using
        ovoid in PG(3,Â 256) [i]
2. OOA(128²², 2796201, S₁₂₈, 3, 7), using
  - OOA 3-folding [i] based on OA(128²², large, S₁₂₈, 7), using
    - discarding parts of the base [i] based on linear OA(256¹⁹, large, F₂₅₆, 7) (dual of [large, large−19, 8]-code), using
      - the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 256³âˆ’1, defining interval IÂ =Â [0,6], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 8 [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.