MinT - Information on Result #1837912

Information on Result #1837912

OOA(128⁶¹, 2097407, S₁₂₈, 4, 15), using OOA 2-folding based on OOA(128⁶¹, 4194814, S₁₂₈, 2, 15), using

discarding factors based on OOA(128⁶¹, 4194815, S₁₂₈, 2, 15), using
- discarding parts of the base [i] based on linear OOA(256⁵³, 4194815, F₂₅₆, 2, 15) (dual of [(4194815, 2), 8389577, 16]-NRT-code), using
  - (u,Â u+v)-construction [i] based on
    1. linear OOA(256¹⁰, 514, F₂₅₆, 2, 7) (dual of [(514, 2), 1018, 8]-NRT-code), using
      - (u,Â u+v)-construction [i] based on
        linear OOA(256³, 257, F₂₅₆, 2, 3) (dual of [(257, 2), 511, 4]-NRT-code), using
        extended Reedâ€“Solomon NRT-code RS_e(2;511,256) [i]
        linear OOA(256⁷, 257, F₂₅₆, 2, 7) (dual of [(257, 2), 507, 8]-NRT-code), using
        extended Reedâ€“Solomon NRT-code RS_e(2;507,256) [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 s, k and t, m and s, m and t.

Other Results with Identical Parameters

None.

Depending Results

None.