MinT - Information on Result #2528712

Information on Result #2528712

OOA(128⁷⁸, large, S₁₂₈, 2, 15), using 128¹ times duplication based on OOA(128⁷⁷, large, S₁₂₈, 2, 15), using

3 times NRT-code embedding in larger space [i] based on OOA(128⁷¹, 8388602, S₁₂₈, 2, 15), using
- discarding parts of the base [i] based on linear OOA(256⁶², 8388602, F₂₅₆, 2, 15) (dual of [(8388602, 2), 16777142, 16]-NRT-code), using
  - (u,Â u+v)-construction [i] based on
    1. linear OOA(256¹⁹, 4194301, F₂₅₆, 2, 7) (dual of [(4194301, 2), 8388583, 8]-NRT-code), using
      - OOA 2-folding [i] based on linear OA(256¹⁹, 8388602, F₂₅₆, 7) (dual of [8388602, 8388583, 8]-code), using
        discarding factors / shortening the dual code 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]
    2. linear OOA(256⁴³, 4194301, F₂₅₆, 2, 15) (dual of [(4194301, 2), 8388559, 16]-NRT-code), using
      - OOA 2-folding [i] based on linear OA(256⁴³, 8388602, F₂₅₆, 15) (dual of [8388602, 8388559, 16]-code), using
        discarding factors / shortening the dual code based on linear OA(256⁴³, large, F₂₅₆, 15) (dual of [large, large−43, 16]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 256³âˆ’1, defining interval IÂ =Â [0,14], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [i]

Mode: Constructive.

Optimality

Show details for fixed k and m, k and t, m and t.

Other Results with Identical Parameters

None.

Depending Results

None.