MinT - Information on Result #1837789

Information on Result #1837789

OOA(128³⁴, 2113535, S₁₂₈, 4, 8), using OOA 2-folding based on OOA(128³⁴, 4227070, S₁₂₈, 2, 8), using

(u,Â u+v)-construction [i] based on
1. OOA(128⁸, 32769, S₁₂₈, 2, 4), using
  - OOA 2-folding [i] based on OA(128⁸, 65538, S₁₂₈, 4), using
    - discarding parts of the base [i] based on linear OA(256⁷, 65538, F₂₅₆, 4) (dual of [65538, 65531, 5]-code), using
      - constructionÂ X applied to C_e(3) âŠ‚ C_e(2) [i] based on
        linear OA(256⁷, 65536, F₂₅₆, 4) (dual of [65536, 65529, 5]-code), using an extension C_e(3) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,3], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 4 [i]
        linear OA(256⁵, 65536, F₂₅₆, 3) (dual of [65536, 65531, 4]-code or 65536-cap in PG(4,256)), using an extension C_e(2) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,2], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 3 [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(128²⁶, 4194301, S₁₂₈, 2, 8), using
  - OOA 2-folding [i] based on OA(128²⁶, 8388602, S₁₂₈, 8), using
    - discarding factors based on OA(128²⁶, large, S₁₂₈, 8), using
      - discarding parts of the base [i] based on linear OA(256²², large, F₂₅₆, 8) (dual of [large, large−22, 9]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 256³âˆ’1, defining interval IÂ =Â [0,7], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 9 [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.