MinT - Information on Result #1837852

Information on Result #1837852

OOA(128⁵², 2113535, S₁₂₈, 4, 12), using OOA 2-folding based on OOA(128⁵², 4227070, S₁₂₈, 2, 12), using

(u,Â u+v)-construction [i] based on
1. OOA(128¹³, 32769, S₁₂₈, 2, 6), using
  - OOA 2-folding [i] based on OA(128¹³, 65538, S₁₂₈, 6), using
    - discarding parts of the base [i] based on linear OA(256¹¹, 65538, F₂₅₆, 6) (dual of [65538, 65527, 7]-code), using
      - constructionÂ X applied to C_e(5) âŠ‚ C_e(4) [i] based on
        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(256⁹, 65536, F₂₅₆, 5) (dual of [65536, 65527, 6]-code), using an extension C_e(4) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,4], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 5 [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(128³⁹, 4194301, S₁₂₈, 2, 12), using
  - OOA 2-folding [i] based on OA(128³⁹, 8388602, S₁₂₈, 12), using
    - discarding factors based on OA(128³⁹, large, S₁₂₈, 12), using
      - discarding parts of the base [i] based on linear OA(256³⁴, large, F₂₅₆, 12) (dual of [large, large−34, 13]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 256³âˆ’1, defining interval IÂ =Â [0,11], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [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.